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.