Detecting change points in the stress-strength reliability P(X < Y)

Abstract

We address the statistical problem of detecting change points in the stress‐strength reliability R=P(X < Y) in a sequence of paired variables (X,Y). Without specifying their underlying distributions, we embed this nonparametric problem into a parametric framework and apply the maximum likelihood method via a dynamic programming approach to determine the locations of the change points in R. Under some mild conditions, we show the consistency and asymptotic properties of the procedure to locate the change points. Simulation experiments reveal that, in comparison with existing parametric and nonparametric change‐point detection methods, our proposed method performs well in detecting both single and multiple change points in R in terms of the accuracy of the location estimation and the computation time. Applications to real data demonstrate the usefulness of our proposed methodology for detecting the change points in the stress‐strength reliability R. Supplementary materials are available online.