Version 11 Profilers “The real voyage of discovery consists not in seeking new landscapes, but in having new eyes.” Marcel Proust JMP, A Business Unit of SAS SAS Campus Drive Cary, NC 27513 The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2013. JMP® 11 Profilers. Cary, NC: SAS Institute Inc. JMP® 11 Profilers Copyright © 2013, SAS Institute Inc., Cary, NC, USA ISBN 978-1-61290-666-9 All rights reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a Web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. 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Get the Most from JMP® Whether you are a first-time or a long-time user, there is always something to learn about JMP. Visit JMP.com to find the following: • live and recorded webcasts about how to get started with JMP • video demos and webcasts of new features and advanced techniques • details on registering for JMP training • schedules for seminars being held in your area • success stories showing how others use JMP • a blog with tips, tricks, and stories from JMP staff • a forum to discuss JMP with other users http://www.jmp.com/getstarted/ Contents Profilers 1 Learn about JMP Documentation and Additional Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Formatting Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 JMP Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 JMP Documentation Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 JMP Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Additional Resources for Learning JMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Tutorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Sample Data Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Learn about Statistical and JSL Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Learn JMP Tips and Tricks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Tooltips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 JMP User Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 JMPer Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 JMP Books by Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 The JMP Starter Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Introduction to Profilers Visualize Response Surfaces and Optimize Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Introduction to Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Profiling Features in JMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Profiler Explore Cross Sections of Responses across Each Factor . . . . . . . . . . . . . . . . . . . . . . . . . 27 Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Interpreting the Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Profiler Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Prediction Profiler Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Desirability Profiling and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 8 Profilers About Desirability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Using the Desirability Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 The Desirability Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Example of Desirability Profiling for Multiple Responses . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Assess Variable Importance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Special Profiler Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Propagation of Error Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Customized Desirability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Mixture Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Expanding Intermediate Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Assess Variable Importance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4 Contour Profiler Explore Contours of Responses across Two Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Contour Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Contour Profiler Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Locking Mixture Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Constraint Shading Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5 Surface Plot Explore Contours of Responses across Three Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Surface Plot Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Launch the Surface Plot Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Plotting a Single Mathematical Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Plotting Points Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Plotting a Formula from a Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Isosurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Surface Plot Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Appearance Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Independent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Dependent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Surface Plot Controls and Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Rotate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 9 Profilers Axis Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Lights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Sheet or Surface Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Other Properties and Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Keyboard Shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6 Mixture Profiler Explore Factor Effects using Ternary Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Mixture Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Explanation of Ternary Plot Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Mixture Profiler Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Single Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Multiple Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 7 Custom Profiler Explore Response Surfaces Using a Numerical Calculator . . . . . . . . . . . . . . . . . . . . . . . . . 97 Custom Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Custom Profiler Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 8 Simulator Explore the Effects of Variation on Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Simulator Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Example of Running the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Specifying Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Responses Report Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Simulator Report Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Using Specification Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Simulating General Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 The Defect Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Graph Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Expected Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Simulation Method and Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Defect Profiler Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 10 Profilers Stochastic Optimization Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Normal Weighted Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 9 Noise Factors Minimize Noise Variation to Create a Robust Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Noise Factors Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Noise Factors in Other Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 10 Excel Profiler Visualize Models Saved in Microsoft Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Excel Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Running the JMP Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Example of an Excel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Using Linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Resolution of Profile Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Using the Excel Profiler from JMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A References Index Profilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Chapter 1 Learn about JMP Documentation and Additional Resources This chapter includes the following information: • book conventions • JMP documentation • JMP Help • additional resources, such as the following: – other JMP documentation – tutorials – indexes – Web resources Figure 1.1 The JMP Help Home Window on Windows Contents Formatting Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 JMP Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 JMP Documentation Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 JMP Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Additional Resources for Learning JMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Tutorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Sample Data Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Learn about Statistical and JSL Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Learn JMP Tips and Tricks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Tooltips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 JMP User Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 JMPer Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 JMP Books by Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 The JMP Starter Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Chapter 1 Profilers Learn about JMP Formatting Conventions 13 Formatting Conventions The following conventions help you relate written material to information that you see on your screen. • Sample data table names, column names, pathnames, filenames, file extensions, and folders appear in Helvetica font. • Code appears in Lucida Sans Typewriter font. • Code output appears in Lucida Sans Typewriter italic font and is indented farther than the preceding code. • Helvetica bold formatting indicates items that you select to complete a task: – buttons – check boxes – commands – list names that are selectable – menus – options – tab names – text boxes • The following items appear in italics: – words or phrases that are important or have definitions specific to JMP – book titles – variables • Features that are for JMP Pro only are noted with the JMP Pro icon of JMP Pro features, visit http://www.jmp.com/software/pro/. . For an overview Note: Special information and limitations appear within a Note. Tip: Helpful information appears within a Tip. JMP Documentation JMP offers documentation in various formats, from print books and Portable Document Format (PDF) to electronic books (e-books). • Open the PDF versions from the Help > Books menu or from the JMP online Help footers. 14 Learn about JMP JMP Documentation Chapter 1 Profilers • All books are also combined into one PDF file, called JMP Documentation Library, for convenient searching. Open the JMP Documentation Library PDF file from the Help > Books menu. • e-books are available at Amazon, Safari Books Online, and in the Apple iBookstore. • You can also purchase printed documentation on the SAS website: http://support.sas.com/documentation/onlinedoc/jmp/index.html JMP Documentation Library The following table describes the purpose and content of each book in the JMP library. Document Title Document Purpose Document Content Discovering JMP If you are not familiar with JMP, start here. Introduces you to JMP and gets you started creating and analyzing data. Using JMP Learn about JMP data tables and how to perform basic operations. Covers general JMP concepts and features that span across all of JMP, including importing data, modifying columns properties, sorting data, and connecting to SAS. Basic Analysis Perform basic analysis using this document. Describes these Analyze menu platforms: • Distribution • Fit Y by X • Matched Pairs • Tabulate How to approximate sampling distributions using bootstrapping is also included. Chapter 1 Profilers Learn about JMP JMP Documentation Document Title Document Purpose Document Content Essential Graphing Find the ideal graph for your data. Describes these Graph menu platforms: • Graph Builder • Overlay Plot • Scatterplot 3D • Contour Plot • Bubble Plot • Parallel Plot • Cell Plot • Treemap • Scatterplot Matrix • Ternary Plot • Chart Also covers how to create background and custom maps. Profilers Learn how to use interactive profiling tools, which enable you to view cross-sections of any response surface. Covers all profilers listed in the Graph menu. Analyzing noise factors is included along with running simulations using random inputs. Design of Experiments Guide Learn how to design experiments and determine appropriate sample sizes. Covers all topics in the DOE menu. 15 16 Learn about JMP JMP Documentation Chapter 1 Profilers Document Title Document Purpose Document Content Fitting Linear Models Learn about Fit Model platform and many of its personalities. Describes these personalities, all available within the Analyze menu Fit Model platform: Specialized Models Learn about additional modeling techniques. • Standard Least Squares • Stepwise • Generalized Regression • Mixed Model • MANOVA • Loglinear Variance • Nominal Logistic • Ordinal Logistic • Generalized Linear Model Describes these Analyze > Modeling menu platforms: • Partition • Neural • Model Comparison • Nonlinear • Gaussian Process • Time Series • Response Screening The Screening platform in the Analyze > Modeling menu is described in Design of Experiments Guide. Multivariate Methods Read about techniques for analyzing several variables simultaneously. Describes these Analyze > Multivariate Methods menu platforms: • Multivariate • Cluster • Principal Components • Discriminant • Partial Least Squares Chapter 1 Profilers Learn about JMP JMP Documentation Document Title Document Purpose Document Content Quality and Process Methods Read about tools for evaluating and improving processes. Describes these Analyze > Quality and Process menu platforms: Reliability and Survival Methods Consumer Research Learn to evaluate and improve reliability in a product or system and analyze survival data for people and products. Learn about methods for studying consumer preferences and using that insight to create better products and services. • Control Chart Builder and individual control charts • Measurement Systems Analysis • Variability / Attribute Gauge Charts • Capability • Pareto Plot • Diagram Describes these Analyze > Reliability and Survival menu platforms: • Life Distribution • Fit Life by X • Recurrence Analysis • Degradation • Reliability Forecast • Reliability Growth • Reliability Block Diagram • Survival • Fit Parametric Survival • Fit Proportional Hazards Describes these Analyze > Consumer Research menu platforms: • Categorical • Factor Analysis • Choice • Uplift • Item Analysis 17 18 Learn about JMP Additional Resources for Learning JMP Chapter 1 Profilers Document Title Document Purpose Document Content Scripting Guide Learn about taking advantage of the powerful JMP Scripting Language (JSL). Covers a variety of topics, such as writing and debugging scripts, manipulating data tables, constructing display boxes, and creating JMP applications. JSL Syntax Reference Read about many JSL functions on functions and their arguments, and messages that you send to objects and display boxes. Includes syntax, examples, and notes for JSL commands. Note: The Books menu also contains two reference cards that can be printed: The Menu Card describes JMP menus, and the Quick Reference describes JMP keyboard shortcuts. JMP Help JMP Help is an abbreviated version of the documentation library that provides targeted information. You can open JMP Help in several ways: • On Windows, press the F1 key to open the Help system window. • Get help on a specific part of a data table or report window. Select the Help tool from the Tools menu and then click anywhere in a data table or report window to see the Help for that area. • Within a JMP window, click the Help button. • Search and view JMP Help on Windows using the Help > Help Contents, Search Help, and Help Index options. On Mac, select Help > JMP Help. • Search the Help at http://jmp.com/support/help/ (English only). Additional Resources for Learning JMP In addition to JMP documentation and JMP Help, you can also learn about JMP using the following resources: • Tutorials (see “Tutorials” on page 19) • Sample data (see “Sample Data Tables” on page 19) • Indexes (see “Learn about Statistical and JSL Terms” on page 19) Chapter 1 Profilers Learn about JMP Additional Resources for Learning JMP • Tip of the Day (see “Learn JMP Tips and Tricks” on page 20) • Web resources (see “JMP User Community” on page 20) • JMPer Cable technical publication (see “JMPer Cable” on page 20) • Books about JMP (see “JMP Books by Users” on page 21) • JMP Starter (see “The JMP Starter Window” on page 21) 19 Tutorials You can access JMP tutorials by selecting Help > Tutorials. The first item on the Tutorials menu is Tutorials Directory. This opens a new window with all the tutorials grouped by category. If you are not familiar with JMP, then start with the Beginners Tutorial. It steps you through the JMP interface and explains the basics of using JMP. The rest of the tutorials help you with specific aspects of JMP, such as creating a pie chart, using Graph Builder, and so on. Sample Data Tables All of the examples in the JMP documentation suite use sample data. Select Help > Sample Data to do the following actions: • Open the sample data directory. • Open an alphabetized list of all sample data tables. • Find a sample data table within a category. Sample data tables are installed in the following directory: On Windows: C:\Program Files\SAS\JMP\<version_number>\Samples\Data On Macintosh: \Library\Application Support\JMP\<version_number>\Samples\Data In JMP Pro, sample data is installed in the JMPPRO (rather than JMP) directory. Learn about Statistical and JSL Terms The Help menu contains the following indexes: Statistics Index Provides definitions of statistical terms. Lets you search for information about JSL functions, objects, and display boxes. You can also edit and run sample scripts from the Scripting Index. Scripting Index 20 Learn about JMP Additional Resources for Learning JMP Chapter 1 Profilers Learn JMP Tips and Tricks When you first start JMP, you see the Tip of the Day window. This window provides tips for using JMP. To turn off the Tip of the Day, clear the Show tips at startup check box. To view it again, select Help > Tip of the Day. Or, you can turn it off using the Preferences window. See the Using JMP book for details. Tooltips JMP provides descriptive tooltips when you place your cursor over items, such as the following: • Menu or toolbar options • Labels in graphs • Text results in the report window (move your cursor in a circle to reveal) • Files or windows in the Home Window • Code in the Script Editor Tip: You can hide tooltips in the JMP Preferences. Select File > Preferences > General (or JMP > Preferences > General on Macintosh) and then deselect Show menu tips. JMP User Community The JMP User Community provides a range of options to help you learn more about JMP and connect with other JMP users. The learning library of one-page guides, tutorials, and demos is a good place to start. And you can continue your education by registering for a variety of JMP training courses. Other resources include a discussion forum, sample data and script file exchange, webcasts, and social networking groups. To access JMP resources on the website, select Help > JMP User Community. JMPer Cable The JMPer Cable is a yearly technical publication targeted to users of JMP. The JMPer Cable is available on the JMP website: http://www.jmp.com/about/newsletters/jmpercable/ Chapter 1 Profilers Learn about JMP Additional Resources for Learning JMP 21 JMP Books by Users Additional books about using JMP that are written by JMP users are available on the JMP website: http://www.jmp.com/support/books.shtml The JMP Starter Window The JMP Starter window is a good place to begin if you are not familiar with JMP or data analysis. Options are categorized and described, and you launch them by clicking a button. The JMP Starter window covers many of the options found in the Analyze, Graph, Tables, and File menus. • To open the JMP Starter window, select View (Window on the Macintosh) > JMP Starter. • To display the JMP Starter automatically when you open JMP on Windows, select File > Preferences > General, and then select JMP Starter from the Initial JMP Window list. On Macintosh, select JMP > Preferences > Initial JMP Starter Window. 22 Learn about JMP Additional Resources for Learning JMP Chapter 1 Profilers Chapter 2 Introduction to Profilers Visualize Response Surfaces and Optimize Processes Profiling is an approach to visualizing response surfaces by seeing what would happen if you change just one or two factors at a time. Essentially, a profile is a cross-section view. The interactive profilers in JMP promote exploring opportunity spaces. In fitting equations to data, the fitting is only half the job. Interpreting the fit, understanding the fitted response surface, and finding factor values to optimize the responses is desirable. Figure 2.1 Examples of Profilers 24 Introduction to Profilers Introduction to Profiling Chapter 2 Profilers Introduction to Profiling It is easy to visualize a response surface with one input factor X and one output factor Y. It becomes harder as more factors and responses are added. The profilers in JMP provide a number of highly interactive cross-sectional views of any response surface. Desirability profiling and optimization features are available to help find good factor settings and produce desirable responses. Most profilers also incorporate multithreading for faster computation. Simulation and defect profiling features are available for when you need to make responses that are robust and high-quality when the factors have variation. Profiling Features in JMP There are several profiler facilities in JMP, accessible from a number of fitting platforms and the main menu under Graph. They are used to profile data column formulas. Table 2.1 Profiler Features Summary Description Features Profiler Shows vertical slices across each factor, holding other factors at current values Desirability, Optimization, Simulator, Propagation of Error Contour Profiler Horizontal slices show contour lines for two factors at a time Simulator Surface Profiler 3-D plots of responses for 2 factors at a time, or a contour surface plot for 3 factors at a time Surface Visualization Mixture Profiler A contour profiler for mixture factors Ternary Plot and Contours Custom Profiler A non-graphical profiler and numerical optimizer General Optimization, Simulator Excel Profiler Visualize models (or formulas) stored in Excel worksheets. Profile using Excel Models Profiler availability is shown in Table 2.2. Chapter 2 Profilers Introduction to Profilers Introduction to Profiling 25 Table 2.2 Where to Find JMP Profilers Location Profiler Contour Profiler Surface Profiler Mixture Profiler Custom Profiler Graph Menu (as a Platform) Yes Yes Yes Yes Yes Fit Model: Least Squares Yes Yes Yes Yes Fit Model: Logistic Yes Fit Model: LogVariance Yes Yes Yes Fit Model: Generalized Linear Yes Yes Yes Nonlinear: Factors and Response Yes Yes Yes Nonlinear: Parameters and SSE Yes Yes Yes Generalized Regression Yes Mixed Model Yes Yes Yes Neural Net Yes Yes Yes Gaussian Process Yes Yes Yes Custom Design Prediction Variance Yes Life Distribution Yes Fit Life by X Yes Choice Yes Yes Yes Yes Note: In this guide, we use the following terms interchangeably: • factor, input variable, X column, independent variable, setting • response, output variable, Y column, dependent variable, outcome The Profiler (with a capital P) is one of several profilers (lowercase p). Sometimes, to distinguish the Profiler from other profilers, we call it the Prediction Profiler. When the profiler is invoked as a platform from the main menu, rather than through a fitting platform, you provide columns with formulas as the Y, Prediction Formula columns. These formulas could have been saved from the fitting platforms. 26 Introduction to Profilers Introduction to Profiling Chapter 2 Profilers Figure 2.2 Profiler Launch Window The columns referenced in the formulas become the X columns (unless the column is also a Y). Y, Prediction Formula The response columns containing formulas. Only used in special cases for modeling derivatives. Details are in the “Noise Factors” chapter on page 133. Noise Factors Expand Intermediate Formulas Tells JMP that if an ingredient column to a formula is a column that itself has a formula, to substitute the inner formula, as long as it refers to other columns. To prevent an ingredient column from expanding, add an Other column property, name it Expand Formula, and assign a value of 0. The Surface Plot platform is discussed in a separate chapter. The Surface Profiler is very similar to the Surface Plot platform, except Surface Plot has more modes of operation. Neither the Surface Plot platform nor the Surface Profiler have some of the capabilities common to other profilers. Fit Group For the REML and Stepwise personalities of the Fit Model platform, if models are fit to multiple Y’s, the results are combined into a Fit Group report. This enables the different Y’s to be profiled in the same Profiler. The Fit Group red-triangle menu has options for launching the joint Profiler. Profilers for the individual Y’s can still be used in the respective Fit Model reports. Fit Group reports are also created when a By variable is specified for a Stepwise analysis. This allows for the separate models to be profiled in the same Profiler. The Fit Group scripting command can be used to fit models in different platforms, and have the individual models profiled in the Profiler. For more details, see the Scripting Guide. Chapter 3 Profiler Explore Cross Sections of Responses across Each Factor The Prediction Profiler, or simply, Profiler, gives you a wealth of information about your model. Use the Prediction Profiler to: • See how your prediction model changes as you change settings of individual factors. • Set desirability goals for your response or responses, and find optimal settings for your factors. • Gauge your model’s sensitivity to changes in the factors, where sensitivity is based on your predictive model. • Assess the important of your factors relative to model predictions, in a way that is independent of the model. • Simulate your response distribution based on specified distributions for both factors and responses, and control various aspects of the appearance of the profiler. Figure 3.1 Profiler for Four Responses with Simulator and Importance Coloring Contents Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Interpreting the Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Profiler Platform Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Prediction Profiler Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Desirability Profiling and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 About Desirability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Using the Desirability Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 The Desirability Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Example of Desirability Profiling for Multiple Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Assess Variable Importance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Special Profiler Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Propagation of Error Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Customized Desirability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Mixture Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Expanding Intermediate Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Linear Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Assess Variable Importance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter 3 Profilers Profiler Profiler Overview 29 Profiler Overview The Profiler displays profile traces (see Figure 3.2) for each X variable. A profile trace is the predicted response as one variable is changed while the others are held constant at the current values. The Profiler recomputes the profiles and predicted responses (in real time) as you vary the value of an X variable. • The vertical dotted line for each X variable shows its current value or current setting. If the variable is nominal, the x-axis identifies categories. See “Interpreting the Profiles” on page 30, for more details. For each X variable, the value above the factor name is its current value. You change the current value by clicking in the graph or by dragging the dotted line where you want the new current value to be. • The horizontal dotted line shows the current predicted value of each Y variable for the current values of the X variables. • The black lines within the plots show how the predicted value changes when you change the current value of an individual X variable. In fitting platforms, the 95% confidence interval for the predicted values is shown by a dotted blue curve surrounding the prediction trace (for continuous variables) or the context of an error bar (for categorical variables). The Profiler is a way of changing one variable at a time and looking at the effect on the predicted response. Figure 3.2 Illustration of Traces current predicted value of response, changes by dragging a factor value current value of factor, changes by dragging the dotted line 95% confidence interval on the mean response current factor values traces, lines, and error bars show predicted values The Profiler in some situations computes confidence intervals for each profiled column. If you have saved both a standard error formula and a prediction formula for the same column, the Profiler offers to use the standard errors to produce the confidence intervals rather than profiling them as a separate column. 30 Profiler Interpreting the Profiles Chapter 3 Profilers Interpreting the Profiles The illustration in Figure 3.3 describes how to use the components of the Profiler. There are several important points to note when interpreting a prediction profile: • The importance of a factor can be assessed to some extent by the steepness of the prediction trace. If the model has curvature terms (such as squared terms), then the traces might be curved. • If you change a factor’s value, then its prediction trace is not affected, but the prediction traces of all the other factors can change. The Y response line must cross the intersection points of the prediction traces with their current value lines. Note: If there are interaction effects or cross-product effects in the model, the prediction traces can shift their slope and curvature as you change current values of other terms. That is what interaction is all about. If there are no interaction effects, the traces only change in height, not slope or shape. Figure 3.3 Changing One Factor from 0 to 0.75 Drag this line to a new value. before These prediction traces change height. after new current predicted response new current value Prediction profiles are especially useful in multiple-response models to help judge that factor values can optimize a complex set of criteria. Chapter 3 Profilers Profiler Interpreting the Profiles 31 Click a graph or drag the current value line right or left to change the factor’s current value. The response values change as shown by a horizontal reference line in the body of the graph. Double-click in an axis to bring up a window that changes its settings. Thinking about Profiling as Cross-Sectioning In the following example using Tiretread.jmp, look at the response surface of the expression for MODULUS as a function of SULFUR and SILANE (holding SILICA constant). Now look at how a grid that cuts across SILANE at the SULFUR value of 2.25. Note how the slice intersects the surface. If you transfer that down below, it becomes the profile for SILANE. Similarly, note the grid across SULFUR at the SILANE value of 50. The intersection when transferred down to the SULFUR graph becomes the profile for SULFUR. Figure 3.4 Profiler as a Cross-Section Now consider changing the current value of SULFUR from 2.25 to 1.5. 32 Profiler Interpreting the Profiles Chapter 3 Profilers Figure 3.5 Profiler as a Cross-Section In the Profiler, note the new value just moves along the same curve for SULFUR, the SULFUR curve itself does not change. But the profile for SILANE is now taken at a different cut for SULFUR. The profile for SILANE is also a little higher and reaches its peak in the different place, closer to the current SILANE value of 50. Setting or Locking a Factor’s Values If you Alt-click (Option-click on the Macintosh) in a graph, a window prompts you to enter specific settings for the factor. Chapter 3 Profilers Profiler Profiler Platform Options 33 Figure 3.6 Continuous Factor Settings Window For continuous variables, you can specify: Current Value The value used to calculate displayed values in the profiler, equivalent to the red vertical line in the graph. Minimum Setting The minimum value of the factor’s axis. Maximum Value The maximum value of the factor’s axis. Number of Plotted Points Specifies the number of points used in plotting the factor’s prediction traces. Show Show or hide the factor in the profiler. Lock Factor Setting Locks the value of the factor at its current setting. Profiler Platform Options The red triangle menu on the Profiler title bar has the following options: Profiler Shows or hides the Profiler. Contour Profiler Shows or hides the Contour Profiler. Custom Profiler Shows or hides the Custom Profiler. Surface Profiler Shows or hides the Surface Profiler. Mixture Profiler Shows or hides the Mixture Profiler. Enables you to save the Profiler (with reduced functionality) as an Adobe Flash file, which can be imported into presentation and web applications. An HTML page can be saved for viewing the Profiler in a browser. The Save as Flash (SWF) command is not available for categorical responses. For more information about this option, go to http://www.jmp.com/support/swfhelp/. Save for Adobe Flash Platform (.SWF) The Profiler accepts any JMP function, but the Flash Profiler only accepts the following functions: Add, Subtract, Multiply, Divide, Minus, Power, Root, Sqrt, Abs, Floor, Ceiling, Min, Max, Equal, Not Equal, Greater, Less, GreaterorEqual, LessorEqual, Or, And, Not, 34 Profiler Prediction Profiler Options Chapter 3 Profilers Exp, Log, Log10, Sine, Cosine, Tangent, SinH, CosH, TanH, ArcSine, ArcCosine, ArcTangent, ArcSineH, ArcCosH, ArcTanH, Squish, If, Match, Choose. Note: Some platforms create column formulas that are not supported by the Save As Flash option. Show Formulas Opens a JSL window showing all formulas being profiled. Formulas for OPTMODEL Creates code for the OPTMODEL SAS procedure. Hold down CTRL and SHIFT and then select Formulas for OPTMODEL from the red triangle menu. Script Contains options that are available to all platforms. See Using JMP. Prediction Profiler Options The red triangle menu on the Prediction Profiler title bar has the following options: Prop of Error Bars Appears under certain situations. See “Propagation of Error Bars” on page 51. Confidence Intervals Shows or hides the confidence intervals. The intervals are drawn by bars for categorical factors, and curves for continuous factors. These are available only when the profiler is used inside certain fitting platforms. Sensitivity Indicator Shows or hides a purple triangle whose height and direction correspond to the value of the partial derivative of the profile function at its current value. This is useful in large profiles to be able to quickly spot the sensitive cells. Chapter 3 Profilers Profiler Prediction Profiler Options 35 Figure 3.7 Sensitivity Indicators Desirability Functions Shows or hides the desirability functions Desirability is discussed in “Desirability Profiling and Optimization” on page 39. Maximize Desirability Sets the current factor values to maximize the desirability functions. Takes into account the response importance weights. Maximize and Remember Maximizes the desirability functions and remembers the associated settings. Maximization Options Enables you to refine the optimization settings through a window. Figure 3.8 Maximization Options Window Maximize for Each Grid Point Used only if one or more factors are locked. The ranges of the locked factors are divided into a grid, and the desirability is maximized at each grid point. This is useful if the model that you are profiling has categorical factors. Then the optimal condition can be found for each combination of the categorical factors. 36 Profiler Prediction Profiler Options Chapter 3 Profilers Save Desirabilities Saves the three desirability function settings for each response, and the associated desirability values, as a Response Limits column property in the data table. These correspond to the coordinates of the handles in the desirability plots. Set Desirabilities Brings up a window where specific desirability values can be set. Figure 3.9 Response Grid Window Creates a column in the data table with a formula for Desirability. The formula uses the fitting formula when it can, or the response variables when it cannot access the fitting formula. Save Desirability Formula Displays a window for each value allowing you to enter specific values for a factor’s current settings. See the section “Setting or Locking a Factor’s Values” on page 32 for details. Reset Factor Grid Factor Settings Submenu that consists of the following options: Remember Settings adds an outline node to the report that accumulates the values of the current settings each time the Remember Settings command is invoked. Each remembered setting is preceded by a radio button that is used to reset to those settings. Set To Data in Row assigns the values of a data table row to the Profiler. Copy Settings Script and Paste Settings Script enable you to move the current Profiler’s settings to a Profiler in another report. Append Settings to Table appends the current profiler’s settings to the end of the data table. This is useful if you have a combination of settings in the Profiler that you want to add to an experiment in order to do another run. Link Profilers links all the profilers together. A change in a factor in one profiler causes that factor to change to that value in all other profilers, including Surface Plot. This is a global option, set or unset for all profilers. Set Script sets a script that is called each time a factor changes. The set script receives a list of arguments of the form {factor1 = n1, factor2 = n2, ...} For example, to write this list to the log, first define a function Chapter 3 Profilers Profiler Prediction Profiler Options 37 ProfileCallbackLog = Function({arg},show(arg)); Then enter ProfileCallbackLog in the Set Script dialog. Similar functions convert the factor values to global values: ProfileCallbackAssign = Function({arg},evalList(arg)); Or access the values one at a time: ProfileCallbackAccess = Function({arg},f1=arg["factor1"];f2=arg["factor2"]); Unthreaded enables you to change to an unthreaded analysis if multithreading does not work. Produces a new data table with columns for the factors that contain grid values, columns for each of the responses with computed values at each grid point, and the desirability computation at each grid point. Output Grid Table If you have a lot of factors, it is impractical to use the Output Grid Table command, because it produces a large table. A memory allocation message might display for large grid tables. In such cases, you should lock some of the factors, which are held at locked, constant values. To get the window to specify locked columns, Alt- or Option-click inside the profiler graph to get a window that has a Lock Factor Setting check box. Figure 3.10 Factor Settings Window Output Random Table Prompts for a number of runs and creates an output table with that many rows, with random factor settings and predicted values over those settings. This is equivalent to (but much simpler than) opening the Simulator, resetting all the factors to a random uniform distribution, then simulating output. This command is similar to Output Grid Table, except it results in a random table rather than a sequenced one. The prime reason to make uniform random factor tables is to explore the factor space in a multivariate way using graphical queries. This technique is called Filtered Monte Carlo. Suppose you want to see the locus of all factor settings that produce a given range to desirable response settings. By selecting and hiding the points that do not qualify (using 38 Profiler Prediction Profiler Options Chapter 3 Profilers graphical brushing or the Data Filter), you see the possibilities of what is left: the opportunity space yielding the result that you want. Some rows may appear selected and marked with a red dot. These represent the points on the multivariate desirability Pareto Frontier - the points that are not dominated by other points with respect to the desirability of all the factors. Alter Linear Constraints Enables you to add, change, or delete linear constraints. The constraints are incorporated into the operation of Prediction Profiler. See “Linear Constraints” on page 55. Save Linear Constraints Enables you to save existing linear constraints to a table script called Constraint. See“Linear Constraints” on page 55. Enables you to set the default number of levels for each continuous factor. This option is useful when the Profiler is especially large. When calculating the traces for the first time, JMP measures how long it takes. If this time is greater than three seconds, you are alerted that decreasing the Default N Levels speeds up the calculations. Default N Levels Conditional Predictions Appears when random effects are included in the model. The random effects predictions are used in formulating the predicted value and profiles. Simulator Launches the Simulator. The Simulator enables you to create Monte Carlo simulations using random noise added to factors and predictions for the model. A typical use is to set fixed factors at their optimal settings, and uncontrolled factors and model noise to random values. You then find out the rate of responses outside the specification limits. For details see the “Simulator” chapter on page 101. Interaction Profiler Brings up interaction plots that are interactive with respect to the profiler values. This option can help visualize third degree interactions by seeing how the plot changes as current values for the terms are changed. The cells that change for a given term are the cells that do not involve that term directly. Arrange in Rows Enter the number of plots that appear in a row. This option helps you view plots vertically rather than in one wide row. Opens a window where you can reorder the model main effects by dragging them to the desired order. Reorder X Variables Opens a window where you can reorder the responses by dragging them to the desired order. Reorder Y Variables Assess Variable Importance Provides three approaches to calculating indices that measure the importance of factors to the model. These indices are independent of the model type and fitting method. Available only for continuous responses. For details, see “Assess Variable Importance” on page 44. Chapter 3 Profilers Profiler Desirability Profiling and Optimization 39 Desirability Profiling and Optimization Often there are multiple responses measured and the desirability of the outcome involves several or all of these responses. For example, you might want to maximize one response, minimize another, and keep a third response close to some target value. In desirability profiling, you specify a desirability function for each response. The overall desirability can be defined as the geometric mean of the desirability for each response. To use desirability profiling, select Desirability Functions from the Prediction Profiler red triangle menu. Note: If the response column has a Response Limits property, desirability functions are turned on by default. This command appends a new row to the bottom of the plot matrix, dedicated to graphing desirability. The row has a plot for each factor showing its desirability trace, as illustrated in Figure 3.11. It also adds a column that has an adjustable desirability function for each Y variable. The overall desirability measure shows on a scale of zero to one at the left of the row of desirability traces. Figure 3.11 The Desirability Profiler desirability function overall desirability measure desirability traces for each factor desirability scale About Desirability Functions The desirability functions are smooth piecewise functions that are crafted to fit the control points. • The minimize and maximize functions are three-part piecewise smooth functions that have exponential tails and a cubic middle. 40 Profiler Desirability Profiling and Optimization • Chapter 3 Profilers The target function is a piecewise function that is a scale multiple of a normal density on either side of the target (with different curves on each side), which is also piecewise smooth and fit to the control points. These choices give the functions good behavior as the desirability values switch between the maximize, target, and minimize values. For completeness, we implemented the upside-down target also. JMP does not use the Derringer and Suich functional forms. Because they are not smooth, they do not always work well with JMP’s optimization algorithm. The control points are not allowed to reach all the way to zero or one at the tail control points. Using the Desirability Function To use a variable’s desirability function, drag the function handles to represent a response value. As you drag these handles, the changing response value shows in the area labeled Desirability to the left of the plots. The dotted line is the response for the current factor settings. The overall desirability shows to the left of the row of desirability traces. Alternatively, you can select Set Desirabilities to enter specific values for the points. Figure 3.12 shows steps to create desirability settings. Maximize The default desirability function setting is maximize (“higher is better”). The top function handle is positioned at the maximum Y value and aligned at the high desirability, close to 1. The bottom function handle is positioned at the minimum Y value and aligned at a low desirability, close to 0. Figure 3.12 Maximizing Desirability You can designate a target value as “best.” In this example, the middle function handle is positioned at Y = 70 and aligned with the maximum desirability of 1. Y becomes less desirable as its value approaches either 45 or 95. The top and bottom function handles at Y = 45 and Y = 95 are positioned at the minimum desirability close to 0. Target Chapter 3 Profilers Profiler Desirability Profiling and Optimization 41 Figure 3.13 Defining a Target Desirability Minimize The minimize (“smaller is better”) desirability function associates high response values with low desirability and low response values with high desirability. The curve is the maximization curve flipped around a horizontal line at the center of plot. Figure 3.14 Minimizing Desirability Note: Dragging the top or bottom point of a maximize or minimize desirability function across the y-value of the middle point results in the opposite point reflecting. A Minimize becomes a Maximize, and vice versa. The Desirability Profile The last row of plots shows the desirability trace for each factor. The numerical value beside the word Desirability on the vertical axis is the geometric mean of the desirability measures. This row of plots shows both the current desirability and the trace of desirabilities that result from changing one factor at a time. For example, Figure 3.15 shows desirability functions for two responses. You want to maximize ABRASION and minimize MODULUS. The desirability plots indicate that you could increase the desirability by increasing any of the factors. 42 Profiler Desirability Profiling and Optimization Chapter 3 Profilers Figure 3.15 Prediction Profile Plot with Adjusted Desirability and Factor Values Example of Desirability Profiling for Multiple Responses A desirability index becomes especially useful when there are multiple responses. The idea was pioneered by Derringer and Suich (1980), who give the following example. Suppose there are four responses, ABRASION, MODULUS, ELONG, and HARDNESS. Three factors, SILICA, SILANE, and SULFUR, were used in a central composite design. The data are in the Tiretread.jmp table in the sample data folder. Use the RSM For 4 responses script in the data table, which defines a model for the four responses with a full quadratic response surface. The summary tables and effect information appear for all the responses, followed by the prediction profiler shown in Figure 3.16. The desirability functions are as follows: 1. Maximum ABRASION and maximum MODULUS are most desirable. 2. ELONG target of 500 is most desirable. 3. HARDNESS target of 67.5 is most desirable. Chapter 3 Profilers Profiler Desirability Profiling and Optimization 43 Figure 3.16 Profiler for Multiple Responses before Optimization Select Maximize Desirability from the Prediction Profiler red triangle menu to maximize desirability. The results are shown in Figure 3.17. The desirability traces at the bottom decrease everywhere except the current values of the effects, which indicates that any further adjustment could decrease the overall desirability. 44 Profiler Assess Variable Importance Chapter 3 Profilers Figure 3.17 Profiler after Optimization Assess Variable Importance For continuous responses, the Variable Importance report calculates indices that measure the importance of factors in a model in a way that is independent of the model type and fitting method. The fitted model is used only in calculating predicted values. The method estimates the variability in the predicted response based on a range of variation for each factor. If variation in the factor causes high variability in the response, then that effect is important relative to the model. Assess Variable Importance can also be accessed in the Profiler that is obtained through the Graph menu. For statistical details, see “Assess Variable Importance” on page 57. See also Saltelli, 2002. The Assess Variable Importance Report The Assess Variable Importance red triangle menu has three options that address the methodology used in constructing importance indices: For each factor, Monte Carlo samples are drawn from a uniform distribution defined by the minimum and maximum observed values. Use this option Independent Uniform Inputs Chapter 3 Profilers Profiler Assess Variable Importance 45 when you believe that your factors are uncorrelated and that their likely values are uniformly spread over the range represented in the study. Independent Resampled Inputs For each factor, Monte Carlo samples are obtained by resampling its set of observed values. Use this option when you believe that your factors are uncorrelated and that their likely values are not represented by a uniform distribution. Dependent Resampled Inputs Factor values are constructed from observed combinations using a k-nearest neighbors approach, in order to account for correlation. This option treats observed variance and covariance as representative of the covariance structure for your factors. Use this option when you believe that your factors are correlated. Note that this option is sensitive to the number of rows in the data table. If used with a small number of rows, the results can be unreliable. The speed of these algorithms depends on the model evaluation speed. In general, the fastest option is Independent Uniform Inputs and the slowest is Dependent Resampled Inputs. You have the option to Accept Current Indices when the estimation process is unable to complete instantaneously. Note: In the case of independent inputs, variable importance indices are constructed using Monte Carlo sampling. For this reason, you can expect some variation in importance index values from one run to another. Variable Importance Report Each Assess Variable Importance option presents a Summary Report and Marginal Model Plots. When the Assess Variable Importance report opens, the factors in the Profiler are reordered according to their Total Effect importance indices. When there are multiple responses, the factors are reordered according to the Total Effect importance indices in the Overall report. When you run several Variable Importance reports, the factors in the Profiler are ordered according to their Total Effect indices in the most recent report. Summary Report For each response, a table displays the following elements: Column The factor of interest. Main Effect An importance index that reflects the relative contribution of that factor alone, not in combination with other factors. An importance index that reflects the relative contribution of that factor both alone and in combination with other factors. The Total Effect column is displayed as a bar chart. Total Effect Main Effect Std Error The Monte Carlo standard error of the Main Effect’s importance index. This is a hidden column that you can access by right-clicking in the report and selecting 46 Profiler Assess Variable Importance Chapter 3 Profilers Columns > Main Effect Std Error. By default, sampling continues until this error is less than 0.01. Details of the calculation are given in “Variable Importance Standard Errors” on page 58. (Not available for Dependent Resampled Inputs option.) Total Effect Std Error The Monte Carlo standard error of the Total Effect’s importance index. This is a hidden column that you can access by right-clicking in the report and selecting Columns > Total Effect Std Error. By default, sampling continues until this error is less than 0.01. Details of the calculation are given in “Variable Importance Standard Errors” on page 58. (Not available for Dependent Resampled Inputs option.) Weights A plot that shows the Total Effect indices, located to the right of the final column. You can deselect or reselect this plot by right-clicking in the report and selecting Columns > Weights. Proportion of function evaluations with missing values The proportion of Monte Carlo samples for which some combination of inputs results in an inestimable prediction. When the proportion is nonzero, this message appears as a note at the bottom of the table. Note: When you have more than one response, the Summary Report presents an Overall table followed by tables for each response. The importance indices in the Overall report are the averages of the importance indices across all responses. Marginal Model Plots The Marginal Model Plots report (see Figure 3.22) shows a matrix of plots, with a row for each response and columns for the factors. The factors are ordered according to the size of their overall Total Effect importance indices. For a given response and factor, the plot shows the mean response for each factor value, where that mean is taken over all inputs to the calculation of importance indices. These plots differ from profiler plots, which show cross sections of the response. Marginal Model Plots are useful for assessing the main effects of factors. Note that your choice of input methodology impacts the values plotted on marginal model plots. Also, because the plots are based on the generated input settings, the plotted mean responses might not appear as smooth curves. Variable Importance Options The Variable Importance report has the following red-triangle options: Reorder factors by main effect importance Reorders the cells in the Profiler in accordance with the importance indices for the main effects (Main Effect). Reorder factors by total importance Reorders the cells in the Profiler in accordance with the total importance indices for the factors (Total Effect). Chapter 3 Profilers Profiler Assess Variable Importance 47 Colorize Profiler Colors cells in the profiler by Total Effect importance indices using a red to white intensity scale. Note: You can click rows in the Summary Report to select columns in the data table. This can facilitate further analyses. Examples A Neural Network Example The Boston Housing.jmp sample data table contains data on 13 factors that might relate to median home values. You will fit a model using a neural network. Because neural networks do not accommodate formal hypothesis tests, these tests are not available to help assess which variables are important in predicting the response. However, for this purpose, you can use the Assess Variable Importance profiler option. Note that your results will differ from, but should resemble, those shown here. There are two sources of random variability in this example. When you fit the neural network, k-fold cross validation is used. This partitions the data into training and validation sets at random. Also, Monte Carlo sampling is used to calculate the factor importance indices. 1. Open the Boston Housing.jmp sample data table. 2. Select Analyze > Modeling > Neural. 3. Select mvalue from the Select Columns list and click Y, Response. 4. Select all other columns from the Select Columns list and click X, Factor. 5. Click OK. 6. In the Neural Model Launch panel, select KFold from the list under Validation Method. When you select KFold, the Number of Folds defaults to 5. 7. Click Go. 8. From the red triangle menu for the Model NTanH(3) report, select Profiler. The Prediction Profiler is displayed at the very bottom of the report. Note the order of the factors for later comparison. Because the factors are correlated, you take this into account by choosing Dependent Resampled Inputs as the sampling method for assessing variable importance. 9. From the red triangle menu next to Prediction Profiler, select Assess Variable Importance > Dependent Resampled Inputs. The Variable Importance: Dependent Resampled Inputs report appears (Figure 3.18). Check that the Prediction Profiler cells have been reordered by the magnitude of the Total Effect indices in the report. In Figure 3.18, check that the Total Effect importance indices identify rooms and lstat as the factors that have most impact on the predicted response. 48 Profiler Assess Variable Importance Chapter 3 Profilers Figure 3.18 Dependent Resampled Inputs Report You might be interested in comparing the importance indices obtained assuming that the factors are correlated, with those obtained when the factors are assumed independent. 10. From the red triangle menu next to Prediction Profiler, select Assess Variable Importance > Independent Resampled Inputs. The resampled inputs option makes sense in this example, because the distributions involved are not uniform. The Variable Importance: Independent Resampled Inputs report is shown in Figure 3.19. Check that the two factors identified as having the most impact on the predicted values are lstat and rooms. Note that the ordering of their importance indices is reversed from the ordering using Dependent Resampled Inputs. Figure 3.19 Independent Resampled Inputs Report Chapter 3 Profilers Profiler Assess Variable Importance 49 Variable Importance for Multiple Responses The data in the Tiretread.jmp sample data table are the result of a designed experiment where the factors are orthogonal. For this reason, you use importance estimates based on independent inputs. Suppose that you believe that, in practice, factor values vary throughout the design space, rather than assume only the settings defined in the experiment. Then you should choose Independent Uniform Inputs as the sampling scheme for your importance indices. 1. Open the Tiretread.jmp sample data table. 2. Run the script RSM for 4 Responses. The Prediction Profiler is displayed at the very bottom of the report. 3. From the red triangle menu next to Prediction Profiler, select Assess Variable Importance > Independent Uniform Inputs. The Summary Report is shown in Figure 3.20. Because the importance indices are based on random sampling, your estimates might differ slightly from those shown in the figure. The report shows tables for each of the four responses. The Overall table averages the factor importance indices across responses. The factors in the Profiler (Figure 3.21) have been reordered to match their ordering on the Overall table’s Total Effect importance. Figure 3.20 Summary Report for Four Responses 50 Profiler Assess Variable Importance Chapter 3 Profilers 4. From the red triangle menu next to Variable Importance: Independent Uniform Inputs, select Colorize Profiler. Colors from a red to white intensity scale are overlaid on profiler panels to reflect Total Effect importance. For example, you easily see that the most important effect is that of Silane on Hardness. Figure 3.21 Profiler for Four Responses The Marginal Model Plots report (Figure 3.22) shows mean responses for each factor across a uniform distribution of settings for the other two factors. Chapter 3 Profilers Profiler Special Profiler Topics 51 Figure 3.22 Marginal Model Plots for Four Responses Special Profiler Topics Propagation of Error Bars Propagation of error (POE) is important when attributing the variation of the response in terms of variation in the factor values when the factor values are not very controllable. In JMP’s implementation, the Profiler first looks at the factor and response variables to see whether there is a Sigma column property (a specification for the standard deviation of the column, accessed through the Cols > Column Info dialog box). If the property exists, then the Prop of Error Bars command becomes accessible in the Prediction Profiler drop-down menu. This displays the 3σ interval that is implied on the response due to the variation in the factor. 52 Profiler Special Profiler Topics Chapter 3 Profilers Figure 3.23 Propagation of Errors Bars in the Prediction Profiler propagation of error bars The POE is represented in the graph by a green bracket. The bracket indicates the prediction plus or minus three times the square root of the POE variance, which is calculated as: N i=1 2 ∂f- 2 σ 2 × ----- x i ∂x + σ y i where f is the prediction function, xi is the ith factor, and N is the number of factors. Currently, these partial derivatives are calculated by numerical derivatives: centered, with δ=xrange/10000 POE limits increase dramatically in response surface models when you are over a more sloped part of the response surface. One of the goals of robust processes is to operate in flat areas of the response surface so that variations in the factors do not amplify in their effect on the response. Chapter 3 Profilers Profiler Special Profiler Topics 53 Customized Desirability Functions It is possible to use a customized desirability function. For example, suppose you want to maximize using the following function. Figure 3.24 Maximizing Desirability Based on a Function First, create a column called MyDesire that contains the above formula. Then, launch the Profiler using Graph > Profiler and include all the Pred Formula columns and the MyDesire column. Turn on the desirability functions by selecting Desirability Functions from the red-triangle menu. All the desirability functions for the individual effects must be turned off. To do this, first double-click in a desirability plot window, then select None in the window that appears (Figure 3.25). Set the desirability for MyDesire to be maximized. Figure 3.25 Selecting No Desirability Goal At this point, selecting Maximize Desirability uses only the custom MyDesire function. 54 Profiler Special Profiler Topics Chapter 3 Profilers Figure 3.26 Maximized Custom Desirability Desirabilities set to None Set to Maximize so that Maximize Desirability uses this function Mixture Designs When analyzing a mixture design, JMP constrains the ranges of the factors so that settings outside the mixture constraints are not possible. This is why, in some mixture designs, the profile traces appear to turn abruptly. When there are mixture components that have constraints, other than the usual zero-to-one constraint, a new submenu, called Profile at Boundary, appears on the Prediction Profiler red triangle menu. It has the following two options: Turn At Boundaries Lets the settings continue along the boundary of the restraint condition. Stop At Boundaries is maintained. Truncates the prediction traces to the region where strict proportionality Chapter 3 Profilers Profiler Special Profiler Topics 55 Expanding Intermediate Formulas The Profiler launch window has an Expand Intermediate Formulas check box. When this is checked, when the formula is examined for profiling, if it references another column that has a formula containing references to other columns, then it substitutes that formula and profiles with respect to the end references—not the intermediate column references. For example, when Fit Model fits a logistic regression for two levels (say A and B), the end formulas (Prob[A] and Prob[B]) are functions of the Lin[x] column, which itself is a function of another column x. If Expand Intermediate Formulas is selected, then when Prob[A] is profiled, it is with reference to x, not Lin[x]. In addition, using the Expand Intermediate Formulas check box enables the Save Expanded Formulas command in the platform red triangle menu. This creates a new column with a formula, which is the formula being profiled as a function of the end columns, not the intermediate columns. Linear Constraints The Prediction Profiler, Custom Profiler, and Mixture Profiler can incorporate linear constraints into their operations. Linear constraints can be entered in two ways, described in the following sections. Red Triangle Menu Item To enter linear constraints via the red triangle menu, select Alter Linear Constraints from either the Prediction Profiler or Custom Profiler red triangle menu. Choose Add Constraint from the resulting window, and enter the coefficients into the appropriate boxes. For example, to enter the constraint p1 + 2*p2 ≤ 0.9, enter the coefficients as shown in Figure 3.27. As shown, if you are profiling factors from a mixture design, the mixture constraint is present by default and cannot be modified. Figure 3.27 Enter Coefficients Enter coefficients After you click OK, the Profiler updates the profile traces, and the constraint is incorporated into subsequent analyses and optimizations. If you attempt to add a constraint for which there is no feasible solution, a message is written to the log and the constraint is not added. To delete a constraint, enter zeros for all the coefficients. 56 Profiler Special Profiler Topics Chapter 3 Profilers Constraints added in one profiler are not accessible by other profilers until saved. For example, if constraints are added under the Prediction Profiler, they are not accessible to the Custom Profiler. To use the constraint, you can either add it under the Custom Profiler red triangle menu, or use the Save Linear Constraints command described in the next section. Constraint Table Property/Script If you add constraints in one profiler and want to make them accessible by other profilers, use the Save Linear Constraints command, accessible through the platform red triangle menu. For example, if you created constraints in the Prediction Profiler, choose Save Linear Constraints under the Prediction Profiler red triangle menu. The Save Linear Constraints command creates or alters a Table Script called Constraint. An example of the Table Property is shown in Figure 3.28. Figure 3.28 Constraint Table Script Constraint script The Constraint Table Property is a list of the constraints, and is editable. It is accessible to other profilers, and negates the need to enter the constraints in other profilers. To view or edit Constraint, right-click the red triangle menu and select Edit. The contents of the constraint from Figure 3.27 is shown below in Figure 3.29. Figure 3.29 Example Constraint The Constraint Table Script can be created manually by choosing New Script from the red triangle menu beside a table name. Note: When creating the Constraint Table Script manually, the spelling must be exactly “Constraint”. Also, the constraint variables are case sensitive and must match the column name. For example, in Figure 3.29, the constraint variables are p1 and p2, not P1 and P2. The Constraint Table Script is also created when specifying linear constraints when designing an experiment. The Alter Linear Constraints and Save Linear Constraints commands are not available in the Mixture Profiler. To incorporate linear constraints into the operations of the Mixture Profiler, the Constraint Table Script must be created by one of the methods discussed in this section. Chapter 3 Profilers Profiler Statistical Details 57 Statistical Details Assess Variable Importance The details that follow relate to the how the variable importance indices are calculated. Background Denote the function that represents the predictive model by f, and suppose that x 1 , x 2 , ... , x n are the factors, or main effects, in the model. Let y = f ( x 1 , x 2 , ... , x n ) . • The expected value of y, E ( y ) , is defined by integrating y with respect to the joint distribution of x 1 , x 2 , ... , x n . • The variance of y, Var ( y ) , is defined by integrating ( y – E ( y ) ) with respect to the joint distribution of x 1 , x 2 , ... , x n . 2 Main Effect The impact of the main effect x j on y can be described by Var ( E ( y x j ) ) . Here the expectation is taken with respect to the conditional distribution of x 1 , x 2 , ... , x n given x j , and the variance is taken over the distribution of x j . In other words, Var ( E ( y x j ) ) measures the variation, over the distribution of x j , in the mean of y when x j is fixed. It follows that the ratio Var ( E ( y x j ) ) ⁄ Var ( y ) gives a measure of the sensitivity of y to the factor x j . The importance index in the Main Effect column in the Summary Report is an estimate of this ratio (see “Adjustment for Sampling Variation” on page 58). Total Effect The Total Effect column represents the total contribution to the variance of y = f ( x1 , x 2 , ... , x n ) from all terms that involve x j . The calculation of Total Effect depends on the concept of functional decomposition. The function f is decomposed into the sum of a constant and functions that represent the effects of single variables, pairs of variables, and so on. These component functions are analogous to main effects, interaction effects, and higher-order effects. (See Saltelli, 2002, and Sobol, 1993.) Those component functions that include terms containing x j are identified. For each of these, the variance of the conditional expected value is computed. These variances are summed. The sum represents the total contribution to Var ( y ) due to terms that contain x j . For each x j , this sum is estimated using the selected methodology for generating inputs. The importance indices reported in the Total Effect column are these estimates (see “Adjustment for Sampling Variation” on page 58). Consider a simple example with two factors, x 1 and x 2 . Then the Total Effect importance index for x 1 is an estimate of: 58 Profiler Statistical Details Chapter 3 Profilers Var ( E ( y x 1 ) ) + Var ( E ( y x 1 , x 2 ) ) ----------------------------------------------------------------------------------------Var ( y ) Adjustment for Sampling Variation Due to the fact that they are obtained using sampling methods, the Main Effect and Total Effect estimates shown in the Summary Table might have been adjusted. Specifically, if the Total Effect estimate is less than the Main Effect estimate, then the Total Effect importance index is set equal to the Main Effect estimate. If the sum of the Main Effect estimates exceeds one, then these estimates are normalized to sum to one. Variable Importance Standard Errors The standard errors that are provided for independent inputs measure the accuracy of the Monte Carlo replications. Importance indices are computed as follows: • Latin hypercube sampling is used to generate a set of data values. • For each set of data values, main and total effect importance estimates are calculated. • This process is replicated until the estimated standard errors of the Main Effect and Total Effect importance indices for all factors fall below a threshold of 0.01. The standard errors that are reported are the standard error values in effect when the replications terminate. Chapter 4 Contour Profiler Explore Contours of Responses across Two Factors The Contour Profiler shows response contours for two factors at a time. The interactive contour profiling facility is useful for optimizing response surfaces graphically. Figure 4.1 Contour Profiler Example Contents Contour Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Contour Profiler Platform Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Locking Mixture Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Constraint Shading Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Chapter 4 Profilers Contour Profiler Contour Profiler Overview 61 Contour Profiler Overview The Contour Profiler shows response contours for two factors at a time. The interactive contour profiling facility is useful for optimizing response surfaces graphically. Figure 4.2 shows an example of the Contour Profiler for the Tiretread sample data. Figure 4.2 Contour Profiler • There are slider controls and edit fields for both the X and Y variables. • The Current X values generate the Current Y values. The Current X location is shown by the crosshair lines on the graph. The Current Y values are shown by the small red lines in the slider control. • The other lines on the graph are the contours for the responses set by the Y slider controls or by entering values in the Contour column. There is a separately colored contour for each response (4 in this example). • You can enter low and high limits to the responses, which results in a shaded region. To set the limits, you can click and drag from the side zones of the Y sliders or enter values in the Lo Limit or Hi Limit columns. If a response column’s Spec Limits column property has 62 Contour Profiler Contour Profiler Platform Options Chapter 4 Profilers values for Lower Spec Limit or Upper Spec Limit, those values are used as the initial values for Lo Limit and Hi Limit. • If you have more than two factors, use the radio buttons in the upper left of the report to switch the graph to other factors. • Right-click the slider control and select Rescale Slider to change the scale of the slider (and the plot for an active X variable). • For each contour, there is a dotted line in the direction of higher response values, so that you get a sense of direction. • Right-click the color legend for a response (under Response) to change the color for that response. Contour Profiler Platform Options Grid Density Sets the density of the mesh plots (Surface Plots). Graph Updating Gives you the options to update the Contour Profiler Per Mouse Move, which updates continuously, or Per Mouse Up, which waits for the mouse to be released to update. (The difference might not be noticeable on a fast machine.) Surface Plot Hides or shows mesh plots. Contour Label Hides or shows a label for the contour lines. The label colors match the contour colors. Contour Grid Draws contours on the Contour Profiler plot at intervals that you specify. Provides a submenu of commands that enables you to save and transfer the Contour Profiler’s settings to other parts of JMP. Details are in the section “Factor Settings” on page 36. Factor Settings Simulator Launches the Simulator. See the “Simulator” chapter on page 101. Up Dots Shows or hides dotted lines corresponding to each contour. The dotted lines show the direction of increasing response values, so that you get a sense of direction. Set Contours to Current Resets the contour lines to be where the current Y values are located. This means that they will all cross where the crosshairs are on the contour plot and the controls will agree in the Y sliders. Rearranges the X and Y controls horizontally with the X controls on the left or vertical with the X controls at the top. Arrange X Controls Left Hide X Controls Shows or hides the X controls (Factor section). Hide Y Controls Shows or hides the Y controls (Response section). Chapter 4 Profilers Contour Profiler Locking Mixture Values 63 Locking Mixture Values For mixture designs, a Lock column appears in the Contour Profiler (Figure 4.3). This column enables you to lock settings for mixture values so that they are not changed when the mixture needs to be adjusted due to other mixture effects being changed. When locked columns exist, the shaded area for a mixture recognizes the newly restricted area. Figure 4.3 Boxes to Lock Columns Constraint Shading Settings Specifying limits to the Y's shades the areas outside the limits as shown in Figure 4.4. The unshaded white area becomes the feasible region. 64 Contour Profiler Constraint Shading Settings Chapter 4 Profilers Figure 4.4 Settings for Contour Shading Setting appropriate limits on responses illustrates the feasible region If a response column’s Spec Limits column property has values for Lower Spec Limit or Upper Spec Limit, those values are used as the initial values for Lo Limit and Hi Limit. Chapter 5 Surface Plot Explore Contours of Responses across Three Factors The Surface Plot platform functions both as a separate platform and as an option in model fitting platforms. Up to four dependent surfaces can be displayed in the same plot. The dependent variables section, below the plot, has four rows that correspond to the four surfaces. Depending on what you choose to view (sheets, points, isosurfaces, or density grids) and whether you supply a formula variable, different options appear in the dependent variables section. Figure 5.1 Example of a Surface Plot Contents Surface Plot Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Launch the Surface Plot Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Plotting a Single Mathematical Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Plotting Points Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Plotting a Formula from a Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Isosurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Surface Plot Platform Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Appearance Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Independent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Dependent Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Surface Plot Controls and Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Rotate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Axis Settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Lights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Sheet or Surface Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Other Properties and Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Keyboard Shortcuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Chapter 5 Profilers Surface Plot Surface Plot Overview 67 Surface Plot Overview The Surface Plot platform is used to plot points and surfaces in three dimensions. Surface plots are available as a separate platform (Graph > Surface Plot) and as options in many reports (known as the Surface Profiler). Its functionality is similar wherever it appears. The plots can be of points or surfaces. When the surface plot is used as a separate platform (that is, not as a profiler), the points are linked to the data table. The points are clickable, respond to the brush tool, and reflect the colors and markers assigned in the data table. Surfaces can be defined by a mathematical equation, or through a set of points defining a polygonal surface. These surfaces can be displayed smoothly or as a mesh, with or without contour lines. Labels, axes, and lighting are fully customizable. Surface Plot is built using the 3-D scene commands from the JMP Scripting Language (JSL). Complete documentation of the OpenGL-style scene commands is found in the Scripting Guide. In this platform, you can: • Use the mouse to drag the surface to a new position. • Right-click the surface to change the background color or show the virtual ArcBall (which helps position the surface). • Enable hardware acceleration, which can increase performance if it is supported on your system. • Drag lights to different positions, assign them colors, and turn them on and off. Launch the Surface Plot Platform To launch the platform, select Surface Plot from the Graph menu. If there is a data table open, this displays the window in Figure 5.2. If you do not want to use a data table for drawing surfaces plots, click OK without specifying columns. If there is no data table open, you are presented with the default surface plot shown in Figure 5.3. 68 Surface Plot Launch the Surface Plot Platform Chapter 5 Profilers Figure 5.2 Surface Plot Launch Window Specify the columns that you want to plot by putting them in the Columns role. Only numeric variables can be assigned to the Columns role. Variables in the By role produce a separate surface plot for each level of the By variable. When selected, the Scale response axes independently option gives a separate scale to each response on the plot. When not selected, the axis scale for all responses is the same as the scale for the first item entered in the Columns role. Plotting a Single Mathematical Function To produce the graph of a mathematical function without any data points, do not fill in any of the roles on the launch window. Simply click OK to get a default plot, as shown in Figure 5.3. Chapter 5 Profilers Surface Plot Launch the Surface Plot Platform Figure 5.3 Default Surface Plot Select the Show Formula check box to show the formula space. 69 70 Surface Plot Launch the Surface Plot Platform Chapter 5 Profilers The default function shows in the box. To plot your own function, enter it in this box. Plotting Points Only To produce a 3-D scatterplot of points, place the x-, y-, and z-columns in the Columns box. For example, using the Tiretread.jmp data, first select Rows > Clear Row States. Then select Graph > Surface Plot. Assign Silica, Silane, and Sulfur to the Columns role. Click OK. Chapter 5 Profilers Surface Plot Launch the Surface Plot Platform 71 Figure 5.4 3-D Scatterplot Launch and Results Plotting a Formula from a Column To plot a formula (that is, a formula from a column in the data table), place the column in the Columns box. For example, use the Tiretread.jmp data table and select Graph > Surface Plot. Assign Pred Formula ABRASION to the Columns role. Click OK. You do not have to specify the factors for the plot, because the platform automatically extracts them from the formula. 72 Surface Plot Launch the Surface Plot Platform Chapter 5 Profilers Figure 5.5 Formula Launch and Output Note that this only plots the prediction surface. To plot the actual values in addition to the formula, assign the ABRASION and Pred Formula ABRASION to the Columns role. Figure 5.6 shows the completed results. Chapter 5 Profilers Surface Plot Launch the Surface Plot Platform 73 Figure 5.6 Formula and Data Points Launch and Output Isosurfaces Isosurfaces are the 3-D analogy to a 2-D contour plot. An isosurface requires a formula with three independent variables. The Resolution slider determines the n × n × n cube of points that the formula is evaluated over. The Value slider in the Dependent Variable section selects the isosurface (that is, the contour level) value. For example, open the Tiretread.jmp data table and run the RSM for 4 Responses script. This produces a response surface model with dependent variables ABRASION, MODULUS, ELONG, and HARDNESS. Now launch Surface Plot and designate the three prediction columns as those to be plotted. 74 Surface Plot Launch the Surface Plot Platform Chapter 5 Profilers When the report appears, select the Isosurface radio button. Under the Dependent Variables outline node, select Both Sides for all three variables. Figure 5.7 Isosurface of Three Variables Isosurface selected These sliders change the level of the surface. Surfaces are showing. Chapter 5 Profilers Surface Plot Surface Plot Platform Options 75 For the tire tread data, one might set the hardness at a fixed minimum setting and the elongation at a fixed maximum setting. Use the MODULUS slider to see which values of MODULUS are inside the limits set by the other two surfaces. Surface Plot Platform Options The red triangle menu in the main Surface Plot title bar has the following entries. Control Panel Shows or hides the Control Panel. Scale response axes independently Scales response axes independently. See explanation of Figure 5.2 on page 68. Script Contains options that are available to all platforms. See Using JMP. The Control Panel consists of the following groups of options. Appearance Controls The first set of controls enables you to specify the overall appearance of the surface plot. Sheet, points Is the setting for displaying sheets, points, and lines. Isosurface Changes the display to show isosurfaces, described in “Isosurfaces” on page 73. Show formula Shows the formula edit box, allowing you to enter a formula to be plotted. The Resolution slider affects how many points are evaluated for a formula. Too coarse a resolution means a function with a sharp change might not be represented very well, but setting the resolution high makes evaluating and displaying the surface slower. Surface Profiler Appearance Controls in Other Platforms If you select the Surface Profiler from the Fit Model, Nonlinear, Gaussian Process, or Neural platforms, there is an additional option in the Appearance controls called data points are. Choose from the following: Off Turns the data points off. Surface plus Residual Shows the difference between the predicted value and actual value on the surface. Actual Shows the actual data points. Residual Shows the residual values (if they are not off the plot). 76 Surface Plot Surface Plot Platform Options Chapter 5 Profilers Independent Variables The independent variables controls are displayed in Figure 5.8. Figure 5.8 Variables Controls Select the variables for the x- and y-axes. Lock the S scale. Sliders and edit boxes set the current value of each variable. When there are more than two independent variables, you can select which two are displayed on the x- and y-axes using the radio buttons in this panel. The sliders and text boxes set the current values of each variable, which is most important for the variables that are not displayed on the axes. In essence, the plot shows the three-dimensional slice of the surface at the value shown in the text box. Move the slider to see different slices. Lock Z Scale locks the z-axis to its current values. This is useful when moving the sliders that are not on an axis. Grid check boxes activate a grid that is parallel to each axis. The sliders enable you to adjust the placement of each grid. The resolution of each grid can be controlled by adjusting axis settings. For example, Figure 5.9 shows a surface with the X and Y grids activated. Figure 5.9 Activated X and Y Grids Chapter 5 Profilers Surface Plot Surface Plot Platform Options 77 Dependent Variables The dependent variables controls change depending on whether you have selected Sheet, points or Isosurface in the Appearance Controls. Controls for Sheet and Points The Dependent Variables controls are shown in Figure 5.10 with its default menus. Figure 5.10 Dependent Variable Controls Formula Lets you select the formula(s) to be displayed in the plot as surfaces. Point Response Column Lets you select the column that holds values to be plotted as points. Style Menus appear after you have selected a Point Response Column. The style menu lets you choose how those points are displayed, as Points, Needles, a Mesh, Surface, or Off (not at all). Points shows individual points, which change according to the color and marker settings of the row in the data table. Needles draws lines from the x-y plane to the points, or, if a surface is also plotted, connects the surface to the points. Mesh connects the points into a triangular mesh. Surface overlays a smooth, reflective surface on the points. Surface Enables you to show or hide the top or bottom of a surface. If Above only or Below only is selected, the opposite side of the surface is darkened. Slider and check box activate a grid for the dependent variable. Use the slider to adjust the value where the grid is drawn, or enter the value into the Grid Value box above the slider. Grid Controls for Isosurface Most of the controls for Isosurface are identical to those of Sheet, points. Figure 5.11 shows the default controls, illustrating the slightly different presentation. 78 Surface Plot Surface Plot Controls and Settings Chapter 5 Profilers Figure 5.11 Dependent Variable Controls for Isosurfaces Sliders adjust the surface Dependent Variable Options There are several options for the Dependent Variable, accessed through the red triangle menu. Formula Reveals or hides the Formula drop-down list. Surface Reveals or hides the Surface drop-down list. Points Reveals or hides the Point Response Column drop-down list. Response Grid Reveals or hides the Grid controls. Surface Plot Controls and Settings Rotate The plot can be rotated in any direction by dragging it. Drag the plot to rotate it. Figure 5.12 Example of Cursor Position for Rotating Plot Cursor indicates when you can rotate the plot. The Up, Down, Left, and Right arrow keys can also be used to rotate the plot. Chapter 5 Profilers Surface Plot Surface Plot Controls and Settings 79 Axis Settings Double-click an axis to reveal the axis control window shown below. The window enables you to change the Minimum, Maximum, Increment, and tick mark label Format. Like other JMP graphs, the axes can be adjusted, stretched, and compressed using the grabber tool. Place the cursor over an axis to change it to the grabber. Figure 5.13 Grabber Tools Place grabber in the middle of axis to adjust. Place grabber at the end of axis to stretch or compress. Notice the orientation of grabber changes from vertical to horizontal Lights By default, the plot has lights shining on it. There are eight control knobs on the plot for changing the position and color of the lights. This is useful for highlighting different parts of a plot and creating contrast. Four of the eight knobs are show below. 80 Surface Plot Surface Plot Controls and Settings Chapter 5 Profilers Figure 5.14 Control Knobs for Lights Activated light Right-click the border to reset lights. Light is off. Right-click knob to turn it on. Right-click a knob to turn that light on or off. More lights turned on brighten a plot, and fewer lights darken it. Drag a knob to change the position of a light. Change the color of a light by right-clicking on the knob. The default color is white. Sheet or Surface Properties If you are plotting a Sheet, points, right-click the sheet and select Sheet Properties to reveal a window for changing the sheet properties. Figure 5.15 Sheet Properties Window Surface Enables you to show or hide the top or bottom of a surface. If Above only or Below only is selected, the opposite side of the surface is darkened. Fill Type Enables you to color the surface using a solid color, or continuous or discrete gradients. If a gradient is chosen, the Show Legend option appears when you right-click the surface. Enables you to turn on or off a surface mesh, for either the X or Y directions or both. If turned on, the Mesh Color option is revealed allowing you to change the color. Mesh Contour Enables you to turn on or off a contour grid, either above, below, or on the surface. If turned on, the Contour Color option is revealed allowing you to change the color. Chapter 5 Profilers Surface Plot Surface Plot Controls and Settings 81 Limit X and Y to Point Response Column limits the range of the plot to the range of the data in the Point Response Column, if one is activated. If checked, this essentially restricts the plot from extrapolating outside the range of the data in the Point Response Column. The equivalent JSL command for this option is Clip Sheet( Boolean ). You can send this message to a particular response column by appending the number of the response column. For example, Clip Sheet2( 1 ) limits the range of the plot to the range of the data of the second response column. See the Scripting Index in the JMP Help menu for an example. If you are plotting an Isosurface, right-click the surface and select Surface Properties to reveal a similar window. You can modify the surface color, opacity, and toggle a mesh. Other Properties and Commands Right-click anywhere in the plot area to reveal the following options: Show Legend Shows a legend when the surface is colored using gradients. Resets the plot to the original viewpoint. Changes in wall and background color are not affected. Reset Settings Opens a window for changing many plot settings. Hide Lights Border Shows or hides lighting controls. Wall Color Enables you to change the plot wall color. Background Color Rows Enables you to change the plot background color. Enables you to change row colors or markers, and also exclude, hide, and label points. Provides for faster rendering of the display. For example, if the plot redraws slowly when rotating, this option can help it redraw faster. Use Hardware Acceleration Show ArcBall Provides options for using the ArcBall. The ArcBall is a sphere drawn around the plot to help visualize the directions of rotation. 82 Surface Plot Keyboard Shortcuts Chapter 5 Profilers Keyboard Shortcuts The following keyboard shortcuts can be used to manipulate the surface plot. To get the plot back to the original viewpoint, right-click the plot and select Reset. Table 5.1 Surface Plot Keyboard Shortcuts Key Function left, right, up, and down arrows spin Home, End diagonally spin Enter (Return) toggles ArcBall appearance Delete roll counterclockwise Control boost spin speed 10X Shift allows continual spinning Chapter 6 Mixture Profiler Explore Factor Effects using Ternary Plots The Mixture Profiler shows response contours for mixture experiment models, where three or more factors in the experiment are components (ingredients) in a mixture. The Mixture Profiler is useful for visualizing and optimizing response surfaces resulting from mixture experiments. Figure 6.1 Mixture Profiler Example Contents Mixture Profiler Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Explanation of Ternary Plot Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Mixture Profiler Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Linear Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Single Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Multiple Responses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Chapter 6 Profilers Mixture Profiler Mixture Profiler Overview 85 Mixture Profiler Overview The Mixture Profiler shows response contours for mixture experiment models, where three or more factors in the experiment are components (ingredients) in a mixture. The Mixture Profiler is useful for visualizing and optimizing response surfaces resulting from mixture experiments. Figure 6.2 shows an example of the Mixture Profiler for the sample data in Plasticizer.jmp. To generate the graph shown, select Mixture Profiler from the Graph menu. In the resulting Mixture Profiler launch window, assign Pred Formula Y to the Y, Prediction Formula role and click OK. Delete the Lo and Hi limits from p1, p2, and p3. Many of the features shown are the same as those of the Contour Profiler and are described on “Contour Profiler Platform Options” on page 62. Some of the features unique to the Mixture Profiler include: • A ternary plot is used instead of a Cartesian plot. A ternary plot enables you to view three mixture factors at a time. • If you have more than three factors, use the radio buttons at the top left of the Mixture Profiler window to graph other factors. For detailed explanation of radio buttons and plot axes, see “Explanation of Ternary Plot Axes” on page 86 • If the factors have constraints, you can enter their low and high limits in the Lo Limit and Hi Limit columns. This shades non-feasible regions in the profiler. As in Contour Plot, low and high limits can also be set for the responses. 86 Mixture Profiler Explanation of Ternary Plot Axes Chapter 6 Profilers Figure 6.2 Mixture Profiler Radio buttons to choose plot axes Setting these shades the area outside limits Explanation of Ternary Plot Axes The sum of all mixture factor values in a mixture experiment is a constant, usually, and henceforth assumed to be 1. Each individual factor’s value can range between 0 and 1, and three are represented on the axes of the ternary plot. For a three factor mixture experiment in which the factors sum to 1, the plot axes run from a vertex (where a factor’s value is 1 and the other two are 0) perpendicular to the other side (where that factor is 0 and the sum of the other two factors is 1). See Figure 6.3. For example, in Figure 6.3, the proportion of p1 is 1 at the top vertex and 0 along the bottom edge. The tick mark labels are read along the left side of the plot. Similar explanations hold for p2 and p3. For an explanation of ternary plot axes for experiments with more than three mixture factors, see “More than Three Mixture Factors” on page 87. Chapter 6 Profilers Mixture Profiler Explanation of Ternary Plot Axes 87 Figure 6.3 Explanation of p1 Axis. p1 = 1 p1 axis labels for p1 axis p1 = 0 More than Three Mixture Factors The ternary plot can only show three factors at a time. If there are more than three factors in the model that you are profiling, the total of the three on-axis (displayed) factors is 1 minus the total of the off-axis (non-displayed) factors. Also, the plot axes are scaled such that the maximum value a factor can attain is 1 minus the total for the off-axis factors. For example Figure 6.4 shows the Mixture Profiler for an experiment with 5 factors. The Five Factor Mixture.jmp data table is being used, with the Y1 Predicted column as the formula. The on-axis factors are x1, x2 and x3, while x4 and x5 are off-axis. The value for x4 is 0.1 and the value for x5 is 0.2, for a total of 0.3. This means the sum of x1, x2 and x3 has to equal 1 – 0.3 = 0.7. In fact, their Current X values add to 0.7. Also, note that the maximum value for a plot axis is now 0.7, not 1. If you change the value for either x4 or x5, then the values for x1, x2 and x3 change, keeping their relative proportions, to accommodate the constraint that factor values sum to 1. 88 Mixture Profiler Mixture Profiler Platform Options Chapter 6 Profilers Figure 6.4 Scaled Axes to Account for Off-Axis Factors Total Mixture Profiler Platform Options The commands under the Mixture Profiler red triangle menu are explained below. Ref Labels Shows or hides the labels on the plot axes. Ref Lines Shows or hides the grid lines on the plot. Show Points Shows or hides the design points on the plot. This feature is only available if there are no more than three mixture factors. Show Current Value Shows or hides the three-way crosshairs on the plot. The intersection of the crosshairs represents the current factor values. The Current X values above the plot give the exact coordinates of the crosshairs. Show Constraints Shows or hides the shading resulting from any constraints on the factors. Those constraints can be entered in the Lo Limits and Hi Limits columns above the plot, or in the Mixture Column Property for the factors. Up Dots Shows or hides dotted line corresponding to each contour. The dotted lines show the direction of increasing response values, so that you get a sense of direction. Contour Grid Draws contours on the plot at intervals that you specify. Chapter 6 Profilers Mixture Profiler Linear Constraints 89 Remove Contour Grid Removes the contour grid if one is on the plot. Is a submenu of commands that enables you to save and transfer the Mixture Profiler settings to other parts of JMP. Details on this submenu are found in the discussion Factor Settings of the profiler on “Factor Settings” on page 36. Linear Constraints The Mixture Profiler can incorporate linear constraints into its operations. To do this, a Constraint Table Script must be part of the data table. See “Linear Constraints” on page 55 in the “Profiler” chapter for details about creating the Table Script. When using constraints, unfeasible regions are shaded in the profiler. Figure 6.5 shows an example of a mixture profiler with shaded regions due to four constraints. The unshaded portion is the resulting feasible region. The constraints are below: • 4*p2 + p3 ≤ 0.8 • p2 + 1.5*p3 ≤ 0.4 • p1 + 2*p2 ≥ 0.8 • p1 + 2*p2 ≤ 0.95 Figure 6.5 Shaded Regions Due to Linear Constraints Examples Single Response This example, adapted from Cornell (1990), comes from an experiment to optimize the texture of fish patties. The data is in Fish Patty.jmp. The columns Mullet, Sheepshead, and Croaker 90 Mixture Profiler Examples Chapter 6 Profilers represent what proportion of the patty came from that fish type. The column Temperature represents the oven temperature used to bake the patties. The column Rating is the response and is a measure of texture acceptability, where higher is better. A response surface model was fit to the data and the prediction formula was stored in the column Predicted Rating. To launch the Mixture Profiler, select Graph > Mixture Profiler. Assign Predicted Rating to Y, Prediction Formula and click OK. The output should appear as in Figure 6.6. Figure 6.6 Initial Output for Mixture Profiler. The manufacturer wants the rating to be at least 5. Use the slider control for Predicted Rating to move the contour close to 5. Alternatively, you can enter 5 in the Contour edit box to bring the contour to a value of 5. Figure 6.7 shows the resulting contour. Chapter 6 Profilers Mixture Profiler Examples 91 Figure 6.7 Contour Showing a Predicted Rating of 5 The Up Dots shown in Figure 6.7 represent the direction of increasing Predicted Rating. Enter 5 in the Lo Limit edit box. The resulting shaded region shown in Figure 6.8 represents factor combinations that will yield a rating less than 5. To produce patties with at least a rating of 5, the manufacturer can set the factors values anywhere in the feasible (unshaded) region. The feasible region represents the factor combinations predicted to yield a rating of 5 or more. Notice the region has small proportions of Croaker (<10%), mid to low proportions of Mullet (<70%) and mid to high proportions of Sheepshead (>30%). 92 Mixture Profiler Examples Chapter 6 Profilers Figure 6.8 Contour Shading Showing Predicted Rating of 5 or More. Up to this point the fourth factor, Temperature, has been held at 400 degrees. Move the slide control for Temperature and watch the feasible region change. Additional analyses might include: • Optimize the response across all four factors simultaneously. See the “Custom Profiler” chapter on page 97 or “Desirability Profiling and Optimization” on page 39 in the “Profiler” chapter. • Simulate the response as a function of the random variation in the factors and model noise. See the “Simulator” chapter on page 101. Multiple Responses This example uses data from Five Factor Mixture.jmp. There are five continuous factors (x1–x5), one categorical factor (Type), and three responses, Y1, Y2 and Y3. A response surface model is fit to each response and the prediction equations are saved in Y1 Predicted, Y2 Predicted and Y3 Predicted. Launch the Mixture Profiler and assign the three prediction formula columns to the Y, Prediction Formula role, then click OK. Enter 3 in the Contour edit box for Y3 Predicted so the contour shows on the plot. The output appears in Figure 6.9. Chapter 6 Profilers Mixture Profiler Examples 93 Figure 6.9 Initial Output Window for Five Factor Mixture A few items to note about the output in Figure 6.9. • All the factors appear at the top of the window. The mixture factors have low and high limits, which were entered previously as a Column Property. See Using JMP for more information about entering column properties. Alternatively, you can enter the low and high limits directly by entering them in the Lo Limit and Hi Limit boxes. • Certain regions of the plot are shaded in gray to account for the factor limits. • The on-axis factors, x1, x2 and x3, have radio buttons selected. • The categorical factor, Type, has a radio button, but it cannot be assigned to the plot. The current value for Type is L1, which is listed immediately to the right of the Current X box. The Current X box for Type uses a 0 to represent L1. • All three prediction equations have contours on the plot and are differentiated by color. A manufacturer desires to hold Y1 less than 1, hold Y2 greater than 8 and hold Y3 between 4 and 5, with a target of 4.5. Furthermore, the low and high limits on the factors need to be respected. The Mixture Profiler can help you investigate the response surface and find optimal factor settings. Start by entering the response constraints into the Lo Limit and Hi Limit boxes, as shown in Figure 6.10. Colored shading appears on the plot and designates unfeasible regions. The 94 Mixture Profiler Examples Chapter 6 Profilers feasible region remains white (unshaded). Use the Response slider controls to position the contours in the feasible region. Figure 6.10 Response Limits and Shading Response Limits Unshaded Feasible Region The feasible region is small. Use the magnifier tool to zoom in on the feasible region shown with a box in Figure 6.10. The enlarged feasible region is shown in Figure 6.11. Chapter 6 Profilers Mixture Profiler Examples 95 Figure 6.11 Feasible Region Enlarged The manufacturer wants to maximize Y1, minimize Y2 and have Y3 at 4.5. • Use the slider controls or Contour edit boxes for Y1 Predicted to maximize the red contour within the feasible region. Keep in mind the Up Dots show direction of increasing predicted response. • Use the slider controls or Contour edit boxes for Y2 Predicted to minimize the green contour within the unshaded region. • Enter 4.5 in the Contour edit box for Y3 Predicted to bring the blue contour to the target value. The resulting three contours do not all intersect at one spot, so you will have to compromise. Position the three-way crosshairs in the middle of the contours to understand the factor levels that produce those response values. 96 Mixture Profiler Examples Chapter 6 Profilers Figure 6.12 Factor Settings Factor settings As shown in Figure 6.12, the optimal factor settings can be read from the Current X boxes. The factor values above hold for the current settings of x4, x5 and Type. Select Factor Settings > Remember Settings from the Mixture Profiler red triangle menu to save the current settings. The settings are appended to the bottom of the report window and appear as shown below. Figure 6.13 Remembered Settings With the current settings saved, you can now change the values of x4, x5 and Type to see what happens to the feasible region. You can compare the factor settings and response values for each level of Type by referring to the Remembered Settings report. Chapter 7 Custom Profiler Explore Response Surfaces Using a Numerical Calculator The Custom Profiler enables you to optimize factor settings computationally, without graphical output. This is used for large problems that would have too many graphs to visualize well. Figure 7.1 Custom Profiler Example Contents Custom Profiler Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Custom Profiler Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Chapter 7 Profilers Custom Profiler Custom Profiler Overview 99 Custom Profiler Overview The Custom Profiler enables you to optimize factor settings computationally, without graphical output. This is used for large problems that would have too many graphs to visualize well. It has many fields in common with other profilers. The Benchmark field represents the value of the prediction formula based on current settings. Click Reset Benchmark to update the results. The Optimization outline node enables you to specify the formula to be optimized and specifications about the optimization iterations. Click the Optimize button to optimize based on current settings. Figure 7.2 Custom Profiler Custom Profiler Platform Options Is a submenu identical to the one covered on “Factor Settings” on page 36 in the “Profiler” chapter. Factor Settings Log Iterations Outputs iterations to a table. Alter Linear Constraints Allows you to add, change, or delete linear constraints. The constraints are incorporated into the operation of Custom Profiler. See “Linear Constraints” on page 55 in the “Profiler” chapter. Save Linear Constraints Allows you to save existing linear constraints to a Table Property/ Script called Constraint. See“Linear Constraints” on page 55 in the “Profiler” chapter. Simulator Launches the Simulator. See the “Simulator” chapter on page 101. 100 Custom Profiler Custom Profiler Platform Options Chapter 7 Profilers Chapter 8 Simulator Explore the Effects of Variation on Responses Simulation enables you to discover the distribution of model outputs as a function of the random variation in the factors and model noise. The simulation facility in the profilers provides a way to set up the random inputs and run the simulations, producing an output table of simulated values. In the Profiler, the Simulator is integrated into the graphical layout. Factor specifications are aligned below each factor’s profile. A simulation histogram is shown on the right for each response. Figure 8.1 Profiler with Simulator Example Contents Simulator Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Example of Running the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Specifying Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Responses Report Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Simulator Report Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Using Specification Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Simulating General Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 The Defect Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Graph Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Expected Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Simulation Method and Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Defect Profiler Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Stochastic Optimization Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Normal Weighted Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Chapter 8 Profilers Simulator Simulator Overview 103 Simulator Overview Simulation enables you to discover the distribution of model outputs as a function of the random variation in the factors and model noise. The simulation facility in the profilers provides a way to set up the random inputs and run the simulations, producing an output table of simulated values. An example of this facility’s use would be to find out the defect rate of a process that has been fit, and see whether it is robust with respect to variation in the factors. If specification limits have been set in the responses, they are carried over into the simulation output, allowing a prospective capability analysis of the simulated model using new factors settings. In the Profiler, the Simulator is integrated into the graphical layout. Factor specifications are aligned below each factor’s profile. A simulation histogram is shown on the right for each response. 104 Simulator Simulator Overview Chapter 8 Profilers Figure 8.2 Profiler with Simulator In the other profilers, the Simulator is less graphical, and kept separate. There are no integrated histograms, and the interface is textual. However, the internals and output tables are the same. Chapter 8 Profilers Simulator Example of Running the Simulation 105 Example of Running the Simulation Tip: The Make Table and Sequencing options are most useful when you have random values. Sequencing options are available for the following distributions only: Normal, Uniform, and Triangular. Specify the number of runs in the simulation by entering it in the N Runs box. After the factor and response distributions are set, click the Simulate button to run the simulation. Or, use the Make Table button to create a table with N Runs for the number of rows. Each row is populated with a random draw from the specified distributions, and the corresponding response values are computed. If spec limits are given, the table also contains a column specifying whether a row is in or out of spec. Use sequencing to examine how the distribution of the response changes when the mean (sequencing location) and variability (sequencing spread) of the inputs change. Sequencing Example 1. Open the Tiretread.jmp sample data table. 2. Select Graph > Profiler. 3. Select Pred Formula ABRASION and Pred Formula MODULUS and click Y, Prediction Formula. 4. Click OK. 5. From the red triangle menu next to Prediction Profiler, select Simulator. 6. Change each factor to be Random instead of Fixed. 7. Change the N Runs value to 100. 8. Open Simulate to Table then Sequencing. 106 Simulator Example of Running the Simulation Chapter 8 Profilers Figure 8.3 Simulator Settings You want to examine how the responses change when the mean values change. 9. For SILICA, select Sequence Location. Keep the number of steps at 5. Because the mean is 1.25, change the values over a range of 1 (lower) to 2 (upper). 10. For SILANE, select Sequence Location. Keep the number of steps at 5. Because the mean is 50, change the values over a range of 40 (lower) to 50 (upper). 11. For SULFUR, select Sequence Location. Keep the number of steps at 5. Because the mean is 2.25, change the values over a range of 2 (lower) to 3 (upper). Figure 8.4 Sequencing Settings 12. Click Make Table. You can see that the SILICA Mean, SILANE Mean, and SULFUR Mean columns contain five steps for each range of values (Silica Mean is 1, 1.25, 1.5, 1.75, and 2; Silane Mean is 40, 42.5, 45, 47.5, and 50; and so on.) Pred Formula ABRASION and Pred Formula MODULUS values are calculated for each combination of values, so you can see how the responses change as the factor values change. 13. Select Analyze > Distribution. Chapter 8 Profilers Simulator Specifying Factors 107 14. Select Pred Formula ABRASION and SILICA Mean and click Y, Columns. 15. Click OK. Figure 8.5 Distribution of SILICA Mean by Pred Formula ABRASION Click a histogram bar that corresponds to a SILICA mean to see how the prediction formula for ABRASION changes given the selected mean. Specifying Factors Factors (inputs) and responses (outputs) are already given roles by being in the Profiler. Additional specifications for the simulator are on how to give random values to the factors, and add random noise to the responses. For each factor, the choices of how to give values are as follows: Fixed Fixes the factor at the specified value. The initial value is the current value in the profiler, which might be a value obtained through optimization. Random Gives the factor the specified distribution and distributional parameters. See the Using JMP book for descriptions of most of these random functions. If the factor is categorical, then the distribution is characterized by probabilities specified for each category, with the values normalized to sum to 1. Normal weighted is normally distributed with the given mean and standard deviation, but a special stratified and weighted sampling system is used to simulate very rare events far out into the tails of the distribution. This is a good choice when you want to measure very low defect rates accurately. See “Statistical Details” on page 130. Normal truncated is a normal distribution limited by lower and upper limits. Any random realization that exceeds these limits is discarded and the next variate within the limits is 108 Simulator Specifying Factors Chapter 8 Profilers chosen. This is used to simulate an inspection system where inputs that do not satisfy specification limits are discarded or sent back. Normal censored is a normal distribution limited by lower and upper limits. Any random realization that exceeds a limit is just set to that limit, putting a density mass on the limits. This is used to simulate a re-work system where inputs that do not satisfy specification limits are reworked until they are at that limit. Sampled means that JMP selects values at random from that column in the data table. External means that JMP selects values at random from a column in another table. You are prompted to choose the table and column. The Aligned check box is used for two or more Sampled or External sources. When checked, the random draws come from the same row of the table. This is useful for maintaining the correlation structure between two columns. If the Aligned option is used to associate two columns in different tables, the columns must have equal number of rows. In the Profiler, a graphical specification shows the form of the density for the continuous distributions, and provides control points that can be dragged to change the distribution. The drag points for the Normal are the mean and the mean plus or minus one standard deviation. The Normal truncated and censored add points for the lower and upper limits. The Uniform and Triangular have limit control points, and the Triangular adds the mode. Figure 8.6 Distributions Allows you to write your own expression in JMP Scripting Language (JSL) form into a field. This gives you flexibility to make up a new random distribution. For example, you could create a censored normal distribution that guaranteed nonnegative values with an expression like Max(0,RandomNormal(5,2)). In addition, character results are supported, so If(Random Uniform() < 0.2, “M”, “F”) works fine. After entering the expression, click the Reset button to submit the expression. Expression Allows you to generate a multivariate normal for when you have correlated factors. Specify the mean and standard deviation with the factor, and a correlation matrix separately. Multivariate Chapter 8 Profilers Simulator Responses Report Options 109 Figure 8.7 Using a Correlation Matrix Responses Report Options If the model is only partly a function of the factors, and the rest of the variation of the response is attributed to random noise, then you will want to specify this with the responses. The choices are: No Noise Evaluates the response from the model, with no additional random noise added. Obtains the response by adding a normal random number with the specified standard deviation to the evaluated model. Add Random Noise Is distributed like Add Random Noise, but with weighted sampling to enable good extreme tail estimates. Add Random Weighted Noise Add Multivariate Noise Yields a response as follows: A multivariate random normal vector is obtained using a specified correlation structure, and it is scaled by the specified standard deviation and added to the value obtained by the model. Simulator Report Options Toggles histogram update, which sends changes to all histograms shown in the Profiler, so that histograms update with new simulated values when you drag distribution handles. Automatic Histogram Update Defect Profiler Shows the defect rate as an isolated function of each factor. This command is enabled when spec limits are available, as described below. Defect Parametric Profile Shows the defect rate as an isolated function of the parameters of each factor’s distribution. It is enabled when the Defect Profiler is launched. Simulation Experiment Used to run a designed simulation experiment on the locations of the factor distributions. A window appears, allowing you to specify the number of design points, the portion of the factor space to be used in the experiment, and which factors to 110 Simulator Simulator Report Options Chapter 8 Profilers include in the experiment. For factors not included in the experiment, the current value shown in the Profiler is the one used in the experiment. The experimental design is a Latin Hypercube. The output has one row for each design point. The responses include the defect rate for each response with spec limits, and an overall defect rate. After the experiment, it would be appropriate to fit a Gaussian Process model on the overall defect rate, or a root or a logarithm of it. A simulation experiment does not sample the factor levels from the specified distributions. As noted above, the design is a Latin Hypercube. At each design point, N Runs random draws are generated with the design point serving as the center of the random draws, and the shape and variability coming from the specified distributions. Spec Limits Shows or edits specification limits. N Strata Is a hidden option accessible by holding down the Shift key before clicking the Simulator red triangle menu. This option enables you to specify the number of strata in Normal Weighted. For more information also see “Statistical Details” on page 130. Set Random Seed Is a hidden option accessible by holding down the Shift key before clicking the Simulator red triangle menu. This option enables you to specify a seed for the simulation starting point. This enables the simulation results to be reproducible, unless the seed is set to zero. The seed is set to zero by default. If the seed is nonzero, then the latest simulation results are output if the Make Table button is clicked. Using Specification Limits The profilers support specification limits on the responses, providing a number of features • In the Profiler, if you do not have the Response Limits property set up in the input data table to provide desirability coordinates, JMP looks for a Spec Limits property and constructs desirability functions appropriate to those Spec Limits. • If you use the Simulator to output simulation tables, JMP copies Spec Limits to the output data tables, making accounting for defect rates and capability indices easy. • Adding Spec Limits enables a feature called the Defect Profiler. In the following example, we assume that the following Spec Limits have been specified. Table 8.1 Spec Limits for Tiretread.jmp Data Table Response LSL Abrasion 110 2000 Modulus Elong USL 350 550 Chapter 8 Profilers Simulator Simulator Report Options 111 Table 8.1 Spec Limits for Tiretread.jmp Data Table (Continued) Response LSL USL Hardness 66 74 To set these limits in the data table, highlight a column and select Cols > Column Info. Then, click the Column Properties button and select the Spec Limits property. If you are already in the Simulator in a profiler, another way to enter them is to use the Spec Limits command in the Simulator red triangle menu. Figure 8.8 Spec Limits After entering the spec limits, they are incorporated into the profilers. Click the Save button if you want the spec limits saved back to the data table as a column property. With these specification limits, and the distributions shown in Figure 8.2, click the Simulate button. Notice the spec limit lines in the output histograms. 112 Simulator Simulator Report Options Chapter 8 Profilers Figure 8.9 Spec Limits in the Prediction Profiler spec limit mean Defect Rate report appears Look at the histogram for Abrasion. The lower spec limit is far above the distribution, yet the Simulator is able to estimate a defect rate for it. This despite only having 5000 runs in the simulation. It can do this rare-event estimation when you use a Normal weighted distribution. Note that the Overall defect rate is close to the defect rate for ELONG, indicating that most of the defects are in the ELONG variable. To see this weighted simulation in action, click the Make Table button and examine the Weight column. JMP generates extreme values for the later observations, using very small weights to compensate. Because the Distribution platform handles frequencies better than weights, there is also a column of frequencies, which is simply the weights multiplied by 1012. The output data set contains a Distribution script appropriate to analyze the simulation data completely with a capability analysis. Simulating General Formulas Though the profiler and simulator are designed to work from formulas stored from a model fit, they work for any formula that can be stored in a column. A typical application of simulation is to exercise financial models under certain probability scenarios to obtain the Chapter 8 Profilers Simulator Simulator Report Options 113 distribution of the objectives. This can be done in JMP—the key is to store the formulas into columns, set up ranges, and then conduct the simulation. Outputs (Responses) Inputs (Factors) Table 8.2 Factors and Responses for a Financial Simulation Unit Sales random uniform between 1000 and 2000 Unit Price fixed Unit Cost random normal with mean 2.25 and std dev 0.1 Revenue formula: Unit Sales*Unit Price Total Cost formula: Unit Sales*Unit Cost + 1200 Profit formula: Revenue – Total Cost The following JSL script creates the data table below with some initial scaling data and stores formulas into the output variables. It also launches the Profiler. dt = newTable("Sales Model"); dt<<newColumn("Unit Sales",Values({1000,2000})); dt<<newColumn("Unit Price",Values({2,4})); dt<<newColumn("Unit Cost",Values({2,2.5})); dt<<newColumn("Revenue",Formula(:Unit Sales*:Unit Price)); dt<<newColumn("Total Cost",Formula(:Unit Sales*:Unit Cost + 1200)); dt<<newColumn("Profit",Formula(:Revenue-:Total Cost), Set Property(“Spec Limits”,{LSL(0)})); Profiler(Y(:Revenue,:Total Cost,:Profit), Objective Formula(Profit)); Figure 8.10 Data Table Created from Script Unit Sales*Unit Cost + 1200 Unit Sales*Unit Price Revenue - Total Cost Once they are created, select the Simulator from the Prediction Profiler. Use the specifications from Table 8.2 on page 113 to fill in the Simulator. 114 Simulator Simulator Report Options Chapter 8 Profilers Figure 8.11 Profiler Using the Data Table Now, run the simulation, which produces the following histograms in the Profiler. Figure 8.12 Simulator It looks like we are not very likely to be profitable. By putting a lower specification limit of zero on Profit, the defect report would say that the probability of being unprofitable is 62%. So we raise the Unit Price to $3.25 and rerun the simulation. Now the probability of being unprofitable is down to about 21%. Figure 8.13 Results Chapter 8 Profilers Simulator The Defect Profiler 115 If unit price cannot be raised anymore, you should now investigate lowering your cost, or increasing sales, if you want to further decrease the probability of being unprofitable. The Defect Profiler The defect profiler shows the probability of an out-of-spec output defect as a function of each factor, while the other factors vary randomly. This is used to help visualize which factor’s distributional changes the process is most sensitive to, in the quest to improve quality and decrease cost. Specification limits define what is a defect, and random factors provide the variation to produce defects in the simulation. Both need to be present for a Defect Profile to be meaningful. At least one of the Factors must be declared Random for a defect simulation to be meaningful, otherwise the simulation outputs would be constant. These are specified though the simulator Factor specifications. Important: If you need to estimate very small defect rates, use Normal weighted instead of just Normal. This allows defect rates of just a few parts per million to be estimated well with only a few thousand simulation runs. About Tolerance Design Tolerance Design is the investigation of how defect rates on the outputs can be controlled by controlling variability in the input factors. The input factors have variation. Specification limits are used to tell the supplier of the input what range of values are acceptable. These input factors then go into a process producing outputs, and the customer of the outputs then judges if these outputs are within an acceptable range. Sometimes, a Tolerance Design study shows that spec limits on input are unnecessarily tight, and loosening these limits results in cheaper product without a meaningful sacrifice in quality. In these cases, Tolerance Design can save money. In other cases, a Tolerance Design study might find that either tighter limits or different targets result in higher quality. In all cases, it is valuable to learn which inputs the defect rate in the outputs are most sensitive to. This graph shows the defect rate as a function of each factor as if it were a constant, but all the other factors varied according to their random specification. If there are multiple outputs with Spec Limits, then there is a defect rate curve color-coded for each output. A black curve shows the overall defect rate—this curve is above all the colored curves. 116 Simulator The Defect Profiler Chapter 8 Profilers Figure 8.14 Defect Profiler Overall defect profile. Defect profile for ABRASION. Current center (mean) for factor. Standard deviation of overall defect curve with respect to factor distribution, which shows sensitivity. Expected mean of overall defect curve, with respect to factor distribution. Roughly equal across factors. Graph Scale Defect rates are shown on a cubic root scale, so that small defect rates are shown in some detail even though large defect rates might be visible. A log scale is not used because zero rates are not uncommon and need to be shown. Expected Defects Reported below each defect profile plot is the mean and standard deviation (SD). The mean is the overall defect rate, calculated by integrating the defect profile curve with the specified factor distribution. In this case, the defect rate that is reported below all the factors is estimating the same quantity, the rate estimated for the overall simulation below the histograms (that is, if you clicked the Simulate button). Because each estimate of the rate is obtained in a different way, they might be a little different. If they are very different, you might need to use more simulation runs. In addition, check that the range of the factor scale is wide enough so that the integration covers the distribution well. The standard deviation is a good measure of the sensitivity of the defect rates to the factor. It is quite small if either the factor profile were flat, or the factor distribution has a very small variance. Comparing SD's across factors is a good way to know which factor should get more attention to reducing variation. The mean and SD are updated when you change the factor distribution. This is one way to explore how to reduce defects as a function of one particular factor at a time. You can click and drag a handle point on the factor distribution, and watch the mean and SD change as you Chapter 8 Profilers Simulator Defect Profiler Example 117 drag. However, changes are not updated across all factors until you click the Rerun button to do another set of simulation runs. Simulation Method and Details Assume we want a defect profile for factor X1, in the presence of random variation in X2 and X3. A series of n=N Runs simulation runs is done at each of k points in a grid of equally spaced values of X1. (k is generally set at 17). At each grid point, suppose that there are m defects due to the specification limits. At that grid point, the defect rate is m/n. With normal weighted, these are done in a weighted fashion. These defect rates are connected and plotted as a continuous function of X1. Notes Recalculation The profile curve is not recalculated automatically when distributions change, though the expected value is. It is done this way because the simulations could take a while to run. Profiling does not address the general optimization problem, that of optimizing quality against cost, given functions that represent all aspects of the problem. This more general problem would benefit from a surrogate model and space filling design to explore this space and optimize to it. Limited goals The defect profiles tend to get uneven when they are low. This is due to exaggerating the differences for low values of the cubic scale. If the overall defect curve (black line) is smooth, and the defect rates are somewhat consistent, then you are probably taking enough runs. If the Black line is jagged and not very low, then increase the number of runs. 20,000 runs is often enough to stabilize the curves. Jagged Defect Profiles Defect Profiler Example To show a common workflow with the Defect profiler, we use Tiretread.jmp with the specification limits from Table 8.1. We also give the following random specifications to the three factors. Figure 8.15 Profiler 118 Simulator Defect Profiler Example Chapter 8 Profilers Select Defect Profiler to see the defect profiles. The curves, Means, and SDs will change from simulation to simulation, but will be relatively consistent. Figure 8.16 Defect Profiler The black curve on each factor shows the defect rate if you could fix that factor at the x-axis value, but leave the other features random. Look at the curve for SILICA. As its values vary, its defect rate goes from the lowest 0.001 at SILICA=0.95, quickly up to a defect rate of 1 at SILICA=0.4 or 1.8. However, SILICA is itself random. If you imagine integrating the density curve of SILICA with its defect profile curve, you could estimate the average defect rate 0.033, also shown as the Mean for SILICA. This is estimating the overall defect rate shown under the simulation histograms, but by numerically integrating, rather than by the overall simulation. The Means for the other factors are similar. The numbers are not exactly the same. However, we now also get an estimate of the standard deviation of the defect rate with respect to the variation in SILICA. This value (labeled SD) is 0.055. The standard deviation is intimately related to the sensitivity of the defect rate with respect to the distribution of that factor. Looking at the SDs across the three factors, we see that the SD for SULFUR is higher than the SD for SILICA, which is in turn much higher than the SD for SILANE. This means that to improve the defect rate, improving the distribution in SULFUR should have the greatest effect. A distribution can be improved in three ways: changing its mean, changing its standard deviation, or by chopping off the distribution by rejecting parts that do not meet certain specification limits. In order to visualize all these changes, there is another command in the Simulator red triangle menu, Defect Parametric Profile, which shows how single changes in the factor distribution parameters affect the defect rate. Chapter 8 Profilers Simulator Defect Profiler Example 119 Figure 8.17 Defect Parametric Profile Let’s look closely at the SULFUR situation. You might need to enlarge the graph to see more detail. First, note that the current defect rate (0.03) is represented in four ways corresponding to each of the four curves. For the red curve, Mean Shift, the current rate is where the red solid line intersects the vertical red dotted line. The Mean Shift curve represents the change in overall defect rate by changing the mean of SULFUR. One opportunity to reduce the defect rate is to shift the mean slightly to the left. If you use the crosshair tool on this plot, you see that a mean shift reduces the defect rate to about 0.02. For the blue curve, Std Narrow, the current rate represents where the solid blue line intersects the two dotted blue lines. The Std Narrow curves represent the change in defect rate by changing the standard deviation of the factor. The dotted blue lines represent one standard deviation below and above the current mean. The solid blue lines are drawn symmetrically around the center. At the center, the blue line typically reaches a minimum, representing the defect rate for a standard deviation of zero. That is, if we totally eliminate variation in SULFUR, the defect rate is still around 0.003. This is much better than 0.03. If you look at the other Defect parametric profile curves, you can see that this is better than reducing variation in the other factors, something that we suspected by the SD value for SULFUR. 120 Simulator Defect Profiler Example Chapter 8 Profilers For the green curve, LSL Chop, there are no interesting opportunities in this example, because the green curve is above current defect rates for the whole curve. This means that reducing the variation by rejecting parts with too-small values for SULFUR will not help. For the orange curve, USL Chop, there are good opportunities. Reading the curve from the right, the curve starts out at the current defect rate (0.03), then as you start rejecting more parts by decreasing the USL for SULFUR, the defect rate improves. However, moving a spec limit to the center is equivalent to throwing away half the parts, which might not be a practical solution. Looking at all the opportunities over all the factors, it now looks like there are two good options for a first move: change the mean of SILICA to about 1, or reduce the variation in SULFUR. Because it is generally easier in practice to change a process mean than process variation, the best first move is to change the mean of SILICA to 1. Figure 8.18 Adjusting the Mean of Silica After changing the mean of SILICA, all the defect curves become invalid and need to be rerun. After clicking Rerun, we get a new perspective on defect rates. Chapter 8 Profilers Simulator Stochastic Optimization Example 121 Figure 8.19 Adjusted Defect Rates Now, the defect rate is down to about 0.004, much improved. Further reduction in the defect rate can occur by continued investigation of the parametric profiles, making changes to the distributions, and rerunning the simulations. As the defect rate is decreased further, the mean defect rates across the factors become relatively less reliable. The accuracy could be improved by reducing the ranges of the factors in the Profiler a little so that it integrates the distributions better. This level of fine-tuning is probably not practical, because the experiment that estimated the response surface is probably not at this high level of accuracy. Once the ranges have been refined, you might need to conduct another experiment focusing on the area that you know is closer to the optimum. Stochastic Optimization Example This example is adapted from Box and Draper (1987) and uses Stochastic Optimization.jmp. A chemical reaction converts chemical “A” into chemical “B”. The resulting amount of chemical “B” is a function of reaction time and reaction temperature. A longer time and hotter temperature result in a greater amount of “B”. But, a longer time and hotter temperature also result in some of chemical “B” getting converted to a third chemical “C”. What reaction time and reaction temperature will maximize the resulting amount of “B” and minimize the amount of “A” and “C”? Should the reaction be fast and hot, or slow and cool? 122 Simulator Stochastic Optimization Example Chapter 8 Profilers Figure 8.20 Chemical Reaction The goal is to maximize the resulting amount of chemical “B”. One approach is to conduct an experiment and fit a response surface model for reaction yield (amount of chemical “B”) as a function of time and temperature. But, due to well known chemical reaction models, based on the Arrhenius laws, the reaction yield can be directly computed. The column Yield contains the formula for yield. The formula is a function of Time (hours) and reaction rates k1 and k2. The reaction rates are a function of reaction Temperature (degrees Kelvin) and known physical constants θ1, θ2, θ3, θ4. Therefore, Yield is a function of Time and Temperature. Figure 8.21 Formula for Yield You can use the Profiler to find the maximum Yield. Open Stochastic Optimization.jmp and run the attached script called Profiler. Profiles of the response are generated as follows. Figure 8.22 Profile of Yield To maximize Yield use a desirability function. See the “Desirability Profiling and Optimization” on page 39 in the “Profiler” chapter. One possible desirability function was incorporated in the script. To view the function choose Desirability Functions from the Prediction Profiler red triangle menu. Chapter 8 Profilers Simulator Stochastic Optimization Example 123 Figure 8.23 Prediction Profiler To maximize Yield, select Maximize Desirability from the Prediction Profiler red triangle menu. The Profiler then maximizes Yield and sets the graphs to the optimum value of Time and Temperature. Figure 8.24 Yield Maximum The maximum Yield is approximately 0.62 at a Time of 0.116 hours and Temperature of 539.92 degrees Kelvin, or hot and fast. [Your results might differ slightly due to random starting values in the optimization process. Optimization settings can be modified (made more stringent) by selecting Maximization Options from the Prediction Profiler red triangle menu. Decreasing the Covergence Tolerance will enable the solution to be reproducible.] In a production environment, process inputs cannot always be controlled exactly. What happens to Yield if the inputs (Time and Temperature) have random variation? Furthermore, if Yield has a spec limit, what percent of batches will be out of spec and need to be discarded? The Simulator can help us investigate the variation and defect rate for Yield, given variation in Time and Temperature. Select Simulator from the Prediction Profiler red triangle menu. As shown in Figure 8.25, fill in the factor parameters so that Temperature is Normal weighted with standard deviation of 1, 124 Simulator Stochastic Optimization Example Chapter 8 Profilers and Time is Normal weighted with standard deviation of 0.03. The Mean parameters default to the current factor values. Change the number of runs to 15,000. Yield has a lower spec limit of 0.55, set as a column property, and shows on the chart as a red line. If it does not show by default, enter it by selecting Spec Limits on the Simulator red triangle menu. Figure 8.25 Initial Simulator Settings LSL = 0.55 Mean = factor value number of runs = 15,000 With the random variation set for the input factors, you are ready to run a simulation to study the resulting variation and defect rate for Yield. Click the Simulate button. Chapter 8 Profilers Simulator Stochastic Optimization Example 125 Figure 8.26 Simulation Results mean defective batches below specification defect rate = 5.5% mean and standard deviation The predicted Yield is 0.62, but if the factors have the given variation, the average Yield is 0.60 with a standard deviation of 0.03. The defect rate is about 5.5%, meaning that about 5.5% of batches are discarded. A defect rate this high is not acceptable. What is the defect rate for other settings of Temperature and Time? Suppose you change the Temperature to 535, then set Time to the value that maximizes Yield? Enter settings as shown in Figure 8.27 then click Simulate. 126 Simulator Stochastic Optimization Example Chapter 8 Profilers Figure 8.27 Defect Rate for Temperature of 535 The defect rate decreases to about 1.8%, which is much better than 5.5%. So, what you see is that the fixed (no variability) settings that maximize Yield are not the same settings that minimize the defect rate in the presence of factor variation. By running a Simulation Experiment you can find the settings of Temperature and Time that minimize the defect rate. To do this you simulate the defect rate at each point of a Temperature and Time design, then fit a predictive model for the defect rate and minimize it. Before running the Simulation Experiment, save the factor settings that maximize Yield so you can reference them later. To do this, re-enter the factor settings (Mean and SD) from Figure 8.25 and select Factor Settings > Remember Settings from Prediction Profiler red triangle menu. A window prompts you to name the settings then click OK. The settings are appended to the report window. Figure 8.28 Remembered Settings Select Simulation Experiment from the Simulator red triangle menu. Enter 80 runs, and 1 to use the whole factor space in the experiment. A Latin Hypercube design with 80 design points is chosen within the specified factor space, and N Runs random draws are taken at each of the design points. The design point are the center of the random draws, and the shape and variance of the random draws coming from the factor distributions. A table is created with the results of the experiment. The Overall Defect Rate is given at each design point. You can now fit a model that predicts the defect rate as a function of Temperature and Time. To do this, run the attached Guassian Process script and wait for the results. The Chapter 8 Profilers Simulator Stochastic Optimization Example 127 results are shown below. Your results will be slightly different due to the random draws in the simulation. Figure 8.29 Results of Gaussian Process Model Fit The Gaussian Process platform automatically starts the Prediction Profiler. The desirability function is already set up to minimize the defect rate. To find the settings of Temperature and Time that minimizes the defect rate, select Maximize Desirability from the Prediction Profiler red triangle menu. 128 Simulator Stochastic Optimization Example Chapter 8 Profilers Figure 8.30 Settings for Minimum Defect Rate The settings that minimize the defect rate are approximately Temperature = 527 and Time = 0.27. Select Factor Settings > Copy Settings Script from the Prediction Profiler red triangle menu. Return to the original Profiler report window and select Factor Settings > Paste Settings Script. This sets Temperature and Time to those settings that minimize the defect rate. Use Remember Settings as before to save these new settings. Figure 8.31 Minimum Defect Settings With the new settings in place, click the Simulate button to estimate the defect rate at the new settings. Chapter 8 Profilers Simulator Stochastic Optimization Example 129 Figure 8.32 Lower Defect Rate At the new settings the defect rate is 0.066%, much better than the 5.5% for the settings that maximize Yield. That is a reduction of about 100x. Recall the average Yield from the first settings is 0.60 and the new average is 0.59. The decrease in average Yield of 0.01 is very acceptable when the defect rate decreases by 100x. Because we saved the settings using Remember Settings, we can easily compare the old and new settings. The Differences report summarizes the difference. Click the Remembered Settings radio buttons to view the profiler for each setting. 130 Simulator Statistical Details Chapter 8 Profilers Figure 8.33 Settings Comparison Radio buttons Maximum yield settings Minimum defect settings The chemist now knows what settings to use for a quality process. If the factors have no variation, the settings for maximum Yield are hot and fast. But, if the process inputs have variation similar to what we have simulated, the settings for maximum Yield produce a high defect rate. Therefore, to minimize the defect rate in the presence of factor variation, the settings should be cool and slow. Statistical Details This section contains statistical details for the Simulator profiler. Normal Weighted Distribution JMP uses the multivariate radial strata method for each factor that uses the Normal Weighted distribution. This seems to work better than a number of Importance Sampling methods, as a multivariate Normal Integrator accurate in the extreme tails. First, define strata and calculate corresponding probabilities and weights. For d random factors, the strata are radial intervals as follows. Chapter 8 Profilers Simulator Statistical Details 131 Table 8.3 Strata Intervals Strata Number 0 Inside Distance 0 1 2 i NStrata – 1 Outside Distance d d d + 2d d + 2d d + 2 2d d + ( i – 1 ) 2d d + i 2d previous ∞ The default number of strata is 12. To change the number of strata, a hidden command N Strata is available if you hold the Shift key down while clicking on the red triangle next to Simulator. Increase the sample size as needed to maintain an even number of strata. For each simulation run: 1. Select a strata as mod(i – 1, NStrata) for run i. 2. Determine a random n-dimensional direction by scaling multivariate Normal (0,1) deviates to unit norm. 3. Determine a random distance using a chi-square quantile appropriate for the strata of a random uniform argument. 4. Scale the variates so that the norm is the random distance. 5. Scale and re-center the variates individually to be as specified for each factor. The resulting factor distributions are multivariate normal with the appropriate means and standard deviations when estimated with the right weights. Note that you cannot use the Distribution standard deviation with weights, because it does not estimate the desired value. However, multiplying the weight by a large value, like 1012, and using that as a Freq value results in the correct standard deviation. 132 Simulator Statistical Details Chapter 8 Profilers Chapter 9 Noise Factors Minimize Noise Variation to Create a Robust Process Robust process engineering enables you to produce acceptable products reliably, despite variation in the process variables. Even when your experiment has controllable factors, there is a certain amount of uncontrollable variation in the factors that affects the response. This is called transmitted variation. Factors with this variation are called noise factors. Some factors you cannot control at all, like environmental noise factors. The mean for some factors can be controlled, but not their standard deviation is not controllable. This is often the case for intermediate factors that are output from a different process or manufacturing step. A good approach to making the process robust is to match the target at the flattest place of the noise response surface. Then, the noise has little influence on the process. Mathematically, this is the value where the first derivatives of each response with respect to each noise factor are zero. JMP computes the derivatives for you. Figure 9.1 Noise Factor Example Contents Noise Factors Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Noise Factors in Other Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Chapter 9 Profilers Noise Factors Noise Factors Overview 135 Noise Factors Overview Noise factors (robust process engineering) enables you to produce acceptable products reliably, despite variation in the process variables. Even when your experiment has controllable factors, there is a certain amount of uncontrollable variation in the factors that affects the response. This is called transmitted variation. Factors with this variation are called noise factors. You cannot control some factors, like environmental noise factors. The mean for some factors can be controlled, but their standard deviation is uncontrollable. This is often the case for intermediate factors that are output from a different process or manufacturing step. A good approach to making the process robust is to match the target at the flattest place of the noise response surface. Then, the noise has little influence on the process. Mathematically, this is the value where the first derivatives of each response with respect to each noise factor are zero. JMP computes the derivatives for you. To analyze a model with noise factors: 1. Fit the appropriate model (for example, using the Fit Model platform). 2. Save the model to the data table with the Save > Prediction Formula command. 3. Launch the Profiler (from the Graph menu). 4. Assign the prediction formula to the Y, Prediction Formula role and the noise factors to the Noise Factor role. 5. Click OK. The resulting profiler shows response functions and their appropriate derivatives with respect to the noise factors, with the derivatives set to have maximum desirability at zero. 6. Select Maximize Desirability from the Profiler menu. This finds the best settings of the factors, balanced with respect to minimizing transmitted variation from the noise factors. Example As an example, use the Tiretread.jmp sample data set. This data set shows the results of a tire manufacturer’s experiment whose objective is to match a target value of HARDNESS= 70 based on three factors: SILICA, SILANE, and SULFUR content. Suppose the SILANE and SULFUR content are easily (and precisely) controllable, but SILICA expresses variability that is worth considering. For comparison, first optimize the factors for hardness without considering variation from the noise factor. 1. Select Graph > Profiler to launch the Profiler. 136 Noise Factors Example Chapter 9 Profilers 2. Assign Pred Formula HARDNESS to the Y, Prediction Formula role. 3. Click OK. 4. Select Desirability Functions in the Prediction Profiler menu. 5. Double-click in the Desirability plot to open the Response Goal window. Select Match Target from the list. 6. Select Maximize Desirability to find the optimum factor settings for our target value of HARDNESS. We get the following Profiler display. Notice that the SILICA factor’s optimum value is on a sloped part of a profile curve. This means that variations in SILICA are transmitted to become variations in the response, HARDNESS. Note: You might get different results from these because different combinations of factor values can all hit the target. Figure 9.2 Maximizing Desirability for HARDNESS On a sloped part of the profile curve Now, we would like to not just optimize for a specific target value of HARDNESS, but also be on a flat part of the curve with respect to Silica. So, repeat the process and add SILICA as a noise factor. 1. Select Graph > Profiler. 2. Select Pred Formula HARDNESS and click Y, Prediction Formula. 3. Select SILICA and click Noise Factors. 4. Click OK. 5. Change the Pred Formula Hardness desirability function as before. The resulting profiler has the appropriate derivative of the fitted model with respect to the noise factor, set to be maximized at zero, its flattest point. Chapter 9 Profilers Noise Factors Example 137 Figure 9.3 Derivative of the Prediction Formula with Respect to Silica Derivative set to maximize at zero 6. Select Maximize Desirability to find the optimum values for the process factor, balancing for the noise factor. This time, we have also hit the targeted value of HARDNESS, but our value of SILICA is on its flatter region. This means variation in SILICA does not transmit as much variation to HARDNESS. Figure 9.4 Maximize Desirability 138 Noise Factors Example Chapter 9 Profilers You can see the effect this has on the variance of the predictions by following these steps for each profiler (one without the noise factor, and one with the noise factor): 1. Select Simulator from the platform menu. 2. Assign SILICA to have a random Normal distribution with a standard deviation of 0.05. Figure 9.5 Setting a Random Normal Distribution Random Normal with SD = 0.05 3. Click Simulate. 4. Click the Make Table button under the Simulate to Table node. Doing these steps for both the original and noise-factor-optimal simulations results in two similar data tables, each holding a simulation. In order to make two comparable histograms of the predictions, we need the two prediction columns in a single data table. 5. Copy the Pred Formula HARDNESS column from one of the simulation tables into the other table. They must have different names, like Without Noise Factor and With Noise Factor. 6. Select Analyze > Distribution and assign both prediction columns as Y. 7. When the histograms appear, select Uniform Scaling from the Distribution main title bar. Chapter 9 Profilers Noise Factors Noise Factors in Other Platforms 139 Figure 9.6 Comparison of Distributions with and without Noise Factors The histograms show that there is much more variation in Hardness when the noise factor was not included in the analysis. It is also interesting to note the shape of the histogram when the noise factor was included. In the comparison histograms above, note that the With Noise Factor distribution has data trailing off in only one direction. The predictions are skewed because Hardness is at a minimum with respect to SILICA, as shown in Figure 9.7. Therefore, variation in SILICA can make only HARDNESS increase. When the non-robust solution is used, the variation could be transmitted either way. Figure 9.7 Profiler Showing the Minima of HARDNESS by SILICA Noise Factors in Other Platforms Noise factor optimization is also available in the Contour Profiler, Custom Profiler, and Mixture Profiler. See the“Contour Profiler” chapter on page 59, the “Custom Profiler” chapter on page 97, and the “Mixture Profiler” chapter on page 83. 140 Noise Factors Noise Factors in Other Platforms Chapter 9 Profilers Chapter 10 Excel Profiler Visualize Models Saved in Microsoft Excel The JMP Add-In for Excel uses the JMP Profiler to visualize models (or formulas) stored in Excel worksheets. The Excel add-in is automatically installed when you install JMP. Figure 10.1 Profiler Using Excel Models Example Contents Excel Profiler Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Running the JMP Profiler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Example of an Excel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Using Linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Resolution of Profile Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Using the Excel Profiler from JMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Chapter 10 Profilers Excel Profiler Excel Profiler Overview 143 Excel Profiler Overview The JMP Add-In for Excel uses the JMP Profiler to visualize models (or formulas) stored in Excel worksheets. The Excel add-in is automatically installed when you install JMP. Profiling in the Excel Add-In is a two-step process: 1. Click the Create/Edit Model button (Excel 2007 through 2013) to enter information about the model that JMP needs. This needs to be done only once per model. For more information, click Help in the Create/Edit Model window. 2. Click the Run Model button (Excel 2007 through 2013) to launch the JMP Profiler and run the Excel model. For more information, see “Running the JMP Profiler” on page 143. Note: The Preferences, Data Table, Graph Builder, and Distribution buttons are not needed to profile an Excel model. For more information about these features, see Using JMP. Running the JMP Profiler Once you create the model using the Excel Add-In, you can run it in the JMP Profiler. From the Excel Add-In, perform the following actions: 1. Click the Run Model button (Excel 2007 through 2013). 2. Select the model that you want to run. 3. Click Profile in JMP. Note: To ensure that your original Excel spreadsheet is not altered, JMP runs a hidden copy of Excel in the background that controls all of the Profiler calculations. Example of an Excel Model An Excel model is one or more Excel formulas. Each formula must be a function of one or more other cells. This example uses the Demand.xls file, located within C:\Program Files\SAS\JMP\<version number>\Samples\Import Data). 144 Excel Profiler Example of an Excel Model Chapter 10 Profilers Figure 10.2 Demand Model in Excel The formula is in cell B8, and is a calculation of the Overall Cost associated with having different amounts of product in stock. The formula can be seen in the Formula Bar, and is a function of four cells: • Amount Stocked is the amount of product in stock. • Demand is the customer demand for the product. • Air Freight is the cost per unit to ship additional product by air when the demand exceeds the amount in stock. • Expiration Cost is the cost per unit of disposing of unused product when the demand is less than the amount in stock. The calculations of the formula are as follows: • If Amount Stocked is less than Demand, then the company has to ship additional units, at a cost of (Demand-Amount Stocked) x Air Freight. For example, if the demand is 8, but the company has only 6 in stock, then it has to ship 8-6=2 units at a cost of 2x150=300. • If Amount Stocked is greater than Demand, then the company has to dispose of unused product, at a cost of (Amount Stocked-Demand) x Expiration Cost. For example, if the demand is 5, but the company has 8 in stock, then it has to dispose of 8-5=3 units at a cost of 3x50=150. • If Amount Stocked is equal to Demand, then there is no shipping cost or disposal cost. • There is never both a shipping cost and a disposal cost at the same time. Using the model in Excel, you can get the cost for only a given set of inputs at once. It is difficult to visualize how changing the value of one input affects the output. You can choose a different combination of the inputs to see how the cost is affected, but doing so for many combinations can take a long time. Use the JMP Profiler to simultaneously see the effect of all inputs on the output. Also, you can quickly simulate a range of input combinations to see the resulting range of output values. Chapter 10 Profilers Excel Profiler Example of an Excel Model 145 Figure 10.3 Example of the Profiler Using Excel Models Using Linear Constraints Within the JMP Profiler, you can alter the linear constraints in order to restrict the model input values. You are prompted to save the constraints to the Excel workbook. After constraints are saved to the Excel workbook, whenever the model is profiled from the Excel Add-In, the constraints are incorporated. 1. From the red triangle menu next to Prediction Profiler, select Alter Linear Constraints. 2. Click Add Constraint. 3. Type in the constraining values. 4. Click OK. 5. From the red triangle menu next to Prediction Profiler, select Save Linear Constraints. You are prompted to save the constraints to the Excel workbook. 6. Click Yes. Note: When you save the .xls file in Excel 2007, you might see a compatibility error. If so, click Continue to save the file. The workbook opens in Excel. When you run the model, the constraints are reflected in the JMP Profiler. For more information about linear constraints, see “Linear Constraints” on page 55 in the “Profiler” chapter. Tip: To delete a linear constraint, set all constraint values to zero. Resolution of Profile Lines The Default N Levels option on the red triangle menu next to Prediction Profiler affects the resolution of the profile lines. Note the following information: • This option defaults to 17 when the Profiler runs a model stored in Excel. • This option defaults to 41 when the model is stored directly in JMP. 146 Excel Profiler Statistical Details Chapter 10 Profilers If the same model is stored in both Excel and JMP, then the profile lines can appear differently when the models are profiled. Increasing this value causes the Excel Profiler to run slower. Using the Excel Profiler from JMP Once an Excel file has the model inputs and outputs defined, you can profile the model from within JMP. 1. Select Graph > Excel Profiler. 2. Locate the Excel file containing the model and then click Open. 3. If the Excel file contains multiple models, you are prompted to select the model that you want to profile. Note that the Excel Profiler is also scriptable, as follows: Excel Profiler( "path to workbook", <"model name"> ) ; If more than one model exists, and no model is specified, a window with the list of available models appears. For more information about scripting the Excel Profiler, see the Scripting Guide. Statistical Details Normal Weighted Distribution JMP uses the multivariate radial strata method for each factor that uses the Normal Weighted distribution. This seems to work better than a number of Importance Sampling methods, as a multivariate Normal Integrator accurate in the extreme tails. First, define strata and calculate corresponding probabilities and weights. For d random factors, the strata are radial intervals as follows. Table 10.1 Strata Intervals Strata Number 0 1 2 i Inside Distance 0 Outside Distance d d d + 2d d + 2d d + 2 2d d + ( i – 1 ) 2d d + i 2d Chapter 10 Profilers Excel Profiler Statistical Details 147 Table 10.1 Strata Intervals (Continued) Strata Number NStrata – 1 Inside Distance previous Outside Distance ∞ The default number of strata is 12. To change the number of strata, a hidden command N Strata is available if you hold the Shift key down while clicking on the red triangle next to Simulator. Figure 10.4 Showing the N Strata Menu Option Increase the sample size as needed to maintain an even number of strata. For each simulation run, 1. Select a strata as mod(i – 1, NStrata) for run i. 2. Determine a random n-dimensional direction by scaling multivariate Normal (0,1) deviates to unit norm. 3. Determine a random distance using a chi-square quantile appropriate for the strata of a random uniform argument. 4. Scale the variates so that the norm is the random distance. 5. Scale and re-center the variates individually to be as specified for each factor. The resulting factor distributions are multivariate normal with the appropriate means and standard deviations when estimated with the right weights. Note that you cannot use the Distribution standard deviation with weights, because it does not estimate the desired value. However, multiplying the weight by a large value, like 1012, and using that as a Freq value results in the correct standard deviation. 148 Excel Profiler Statistical Details Chapter 10 Profilers Appendix A References Box, G.E.P. and Draper, N.R. (1987), Empirical Model–Building and Response Surfaces, New York: John Wiley and Sons. Cornell, J.A. (1990), Experiments with Mixtures, Second Edition, New York: John Wiley and Sons. Derringer, D. and Suich, R. (1980), “Simultaneous Optimization of Several Response Variables,” Journal of Quality Technology, 12:4, 214-219. Saltelli, A. (2002), “Making best use of model evaluations to compute sensitivity indices,” Computer Physics Communications, 145, 280-297. Sobol, I.M. (1993), “Sensitivity Estimates for Nonlinear Mathematical Models,” MMCE, 1:4, 407-414. 150 References Appendix A Profilers Index Profilers A E Add Multivariate Noise 109 Add Random Noise 109 Add Random Weighted Noise 109 Alt-click 32 Alter Linear Constraints 38, 99 Append Settings to Table 36 ArcBall 81 Automatic Histogram Update 109 Excel Profiler 143 profiling models stored in 143 Expand Intermediate Formulas 26, 55 Expression 108 C closing JMP Starter window 121 Conditional Predictions 38 Confidence Intervals 34 Constraints 55 Contour Grid 62, 88 Contour Label 62 Contour Profiler 61–135 Copy Settings Script 36 cross-product term 30 current predicted value 29 Current Value 33 current value 29 Custom Profiler 99 D Data Filter 38 Default N Levels 38 Defect Parametric Profile 109, 118 Defect Profiler 115 Defect Profiler 109, 118 Dependent Resampled Inputs 45 desirability confidence curve 29 Desirability Functions 35, 39 desirability trace 39 drag 29, 31, 40, 61 F Factor Settings 36, 99 Filtered Monte Carlo 37 Fish Patty.jmp 89 Fit Group 26 Fit Model platform example 42–44, 61–64 Five Factor Mixture.jmp 92 Fixed 107 G Graph Updating 62 Grid Density 62 H Hardware Acceleration 81 I Independent Resampled Inputs 45 Independent Uniform Inputs 44 interaction effect 30 Interaction Profiler 38 Isosurface 73 J JMP Starter 121 JMP tutorials 119 152 Index Profilers L P Linear Constraints 89 Linear Constraints 55 Link Profilers 36 Lock Factor Setting 33, 37 Lock Z Scale 76 Log Iterations 99 LSL Chop 120 Paste Settings Script 36 Per Mouse Move 62 Per Mouse Up 62 Prediction Profiler 29 profile trace 29 M Make Table 105, 112 Maximization Options 35 Maximize 40 Maximize Desirability 35 Maximize for Each Grid Point 35 Maximum Value 33 mean shift 119 menu tips 120 Mesh 80 Minimize 41 Minimum Setting 33 Mixture Profiler 85 multiple response fitting 30, 42 Multivariate 108 Profiler Assess Variable Importance 44 Dependent Resampled Inputs 45 Independent Resampled Inputs 45 Independent Uniform Inputs 44 Profiler 29 Profilers 23–139 Prop of Error Bars 34, 51 R Random 107 Ref Labels 88 Ref Lines 88 Remember Settings 36, 96 Remove Contour Grid 89 Reset Factor Grid 36 Response Limits 110 Robust Engineering 135–139 N S N Runs 105 N Strata 110, 147 No Noise 109 Noise Factors 135–139 Noise Factors 26 Normal censored 108 Normal Truncated 107 Normal Weighted 146 Normal weighted 107, 112 Number of Plotted Points 33 Sampled 108 Save As Flash (SWF) 33 Save Desirabilities 36 Save Desirability Formula 36 Save Expanded Formulas 55 Save Linear Constraints 38, 99 Sensitivity Indicator 34 Set Desirabilities 36, 40 Set Random Seed 110 Set Script 36 Set To Data in Row 36 Show 33 Show Constraints 88 Show Current Value 88 Show Formulas 34 Show Points 88 Sigma 51 Simulate 116 O opening JMP Starter window 121 Option-click 32 OPTMODEL formulas 34 Output Grid Table 37 Output Random Table 37 Index Profilers Simulation Experiment 109 Simulator 37, 103 Simulator 38 Spec Limits 110–111 Std Narrow 119 Stochastic Optimization.jmp 121 Stop At Boundaries 54 Surface Fill 80 Surface Plot 67 Constants 82 Control Panel 75 Dependent Variables 77 Variables 76 Surface Plot 62 Surface Profiler 67 T Target 40 Tiretread.jmp 31, 70–71, 117, 135 tiretread.jmp 42 tooltips 120 transmitted variation 135 Turn At Boundaries 54 tutorial examples contour profiler 61–64 desirability profile 42–44 tutorials 119 U Up Dots 62, 88 USL Chop 120 V Variable Importance 44 Variable Importance with Dependent Resampled Inputs 45 Variable Importance with Independent Resampled Inputs 45 Variable Importance with Uniform Inputs 44 W-Z Y, Prediction Formula 26 153 154 Index Profilers

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