Version 11
Profilers
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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.
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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
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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.
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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
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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,
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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
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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.
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Chapter 3
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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
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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
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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
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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
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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.
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Chapter 3
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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
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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.
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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
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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
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Chapter 3
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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
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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.
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Chapter 3
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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
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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
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Chapter 3
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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
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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.
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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.
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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
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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.
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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.
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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.
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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
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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
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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%).
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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
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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
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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
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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
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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.
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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
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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.
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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
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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.
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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
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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
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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.
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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.
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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.
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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?
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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.
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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,
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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
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Example
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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.
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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).
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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.
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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.
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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.
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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