Modern Statistical Methods and Uncertainty Quantification for Evaluating Reliability of Nondestructive Evaluation Systems

The reliability of Nondestructive Evaluation (NDE) is an important input for risk analysis for sustainment of aging infrastructure. Reliability has typically been quantified via probability of detection (POD) studies. There are three problems with POD modeling methodologies provided in the most recent guidance on the subject: 1) Current models do not estimate the extremes of a POD curve very well because of the assumption that the POD curve approaches zero as flaw size goes to zero, and the POD curve approaches one as the flaw size goes to infinity. 2) The existing 2-parameter logit/probit models can be misused since there is not a set of diagnostics and procedures that can catch every violation of fundamental assumptis. 3) Data sets from realistic inspections often violate core assumptions in statistical models such as homoscedasticty and linearity, but statistical inference is still needed for the application. Since one of the important inputs to risk assessment is POD, and it\u27s believed that the output of risk analyses can be sensitive to the tail behavior at large flaw sizes, it is worthwhile to consider better estimation procedures for the extremes of a POD curve. In this dissertation, new POD models that include lower and upper asymptotes are proposed to better model tail behavior. Transformations such as Box-Cox are proposed to mitigate violations of homoscedasticity, and bootstrapping is proposed to provide confidence bound calculations for higher order models. A case study is presented where these improvements to POD analysis are incorporated into a risk analysis. Simulation studies a presented to quantify the improvements of this work