Objective Bayesian analysis for generalized exponential stress–strength model

In reliability studies, a stress–strength model is often used to analyze a system that fails whenever the applied stress is greater than the strength. Statistical inference of reliability is widely used in a number of areas, such as engineering, clinical trials, and quality control. In addition to the common stress–strength model with one stress and one strength, the reliability of more complex systems has also been studied. In this study, we consider the reliability of a generalized stress–strength model that consists of a serial system with one stress and multiple strengths. We then develop the probability matching priors and reference priors for a generalized exponential stress–strength model. We demonstrate that the two-group reference prior and Jeffreys prior are not a matching prior. Through a simulation study and real data example, we also demonstrate that the proposed probability matching priors match the target coverage probabilities in a frequentist sense even for a small sample size.