Modern Design and Analysis For Hit/Miss Probability of Detection Studies Using Profile Likelihood Ratio Confidence Intervals

To characterize the capability of an inspection system, indications from the system must be collected over a range of defect sizes. For flaw indications, insufficient sample size, overlap, or evenness between hit and miss indications may cause the probability of detection (POD) estimations to not exist or have high bias. Extensive simulations of representative Lognormal, Weibull, and Uniformly distributed data at varying levels of overlap, evenness, and sample size were fit using four modeling techniques: logistic regression, Firth’s Bias Adjusted Likelihood, the Lasso, and a ranked set sampling method from nonparametric statistics. Profile likelihood ratio confidence intervals were used instead of the standard Wald method to calculate a90/95. The probability of existence and the percent bias of the estimates provide recommendations for the ideal levels of overlap, evenness, modeling technique, and sample size requirements when designing a hit/miss POD study.