Probability of Detection (PoD) Curves Based on Weibull Statistics

Abstract

Probability of detection (PoD) curves are a popular metric for the reliability assessment of Nondestructive Testing (NDT) procedures. However, the classical Berens method for signal response PoD analysis strongly relies on the hypothesis of Gaussian residuals which can be violated in practical conditions. In particular, data from sparse field trials can be scattered and or skewed. Hence, this paper studies the feasibility of assuming a Weibull distribution, which is known for versatility in representing several fundamental statistical states, for regression residuals without modifying the overall Berens framework for PoD curve determination. The proposed ‘Weibull-Berens’ PoD statistics is first shown to compare well with the classical Berens method for an ideal case of Gaussian residuals. The advantages of the method are further demonstrated using a synthesised dataset, as well as a practical case of non-Gaussian residuals arising from reduced number of experimental trials.