Probability of Detection for Dependent Observations: The Repeated Measures Method

Probability of detection (POD) calculations in structural health monitoring (SHM) applications are complicated by the dependency of measurements obtained on the same structure, among other factors. This article presents a repeated measures method to extend POD signal-response modeling to correctly describe a population of repeated measurements while estimating the variance due to dependence in the observations. In particular, equations are presented which develop an autoregressive correlation structure to model continuous observations that are correlated in time. Software implementation of these models is discussed and methodology to simulate correlated datasets is presented. The combination of these tools enables a method of POD estimation in SHM applications through the appropriate mathematical extensions of the statistical modeling.