Curve Fitting for Probability of Detection Data: A 4-Parameter Generalization

The hit - miss data taken from NDE validation and inspector qualification exercises have traditionally been used with logit or probit binary regression models to estimate probability of detection ( POD) curves. These models are specified by functions with two parameters that determine location and shape of the resulting POD expressed in terms of an independent flaw size variable. A generalization of these models is discussed in which two additional parameters are added that allow the POD function range to be confined to a subset of the 0 to 1 interval. Thus the POD curve can have a lower asymptote other than zero and an upper asymptote other than one. The additional parameters model naturally occurring inspection phenomena such as detections and misses independent of flaw size. The relationship of this 4 - parameter model to non - parametric POD estimation is also discussed. Determining the need for, or the desirability of, fitting additional parameters is developed in terms of the statistical significance of the additional parameters. Other strategies for judging the ability of the resultant POD curve from the 4 - parameter fit to more adequately reflect the inspection data are also considered.