GammaVision
®
v7 (A66-BW) 783620H / 1013
If the beta risk error and the alpha risk error are the same (k
1-
α
= k
1-
β
= k), then no matter the value of k and the uncertainty, R is twice the value of factor f:
(178)
If the errors are the same, the term inside the square-root in Eq. 176 is 1.0, thus R is 2.0. The same result can be obtained using Eq. 177, although it is less obvious that this is the case simply by inspecting Eq. 177.
Maximum MDA Ratio
If the uncertainties are extremely small so that A is very large, then the MDA correction factor f should be close to 1.0. From Eq. 177 we see that the MDA ratio R then approaches a value of
2.0. Note that this is true even though the beta and alpha errors are not the same. Therefore, the minimum MDA ratio should be set to 2.0 as well. Under typical conditions, the following are true:
(179)
However, when the uncertainty is increased, A becomes smaller and smaller and f becomes larger and larger (see Eq. 173). The ratio can approach infinity if the denominator for f is zero (A
. 1).
When the uncertainty is further increased, both f (or R) and the MDA become negative.
We can prevent the MDA from going negative or to infinity by reducing the beta risk error so there is an upper limit for the ratio R:
(180)
The steps for limiting the ratio are:
1) Calculate the MDA ratio with Eq. 176, using the original alpha and beta risk error.
2) If the calculated R from Eq. 176 is greater than R
Max
, force the ratio R to the value of R
Max
in
Eq. 177 to calculate an MDA correction factor f
max
as shown below:
(181)
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