Statistical Inference of Wiener Constant-Stress Accelerated Degradation Model with Random Effects

In the field of reliability analysis, the constant-stress accelerated degradation test is one of the most commonly used methods to evaluate a product’s reliability as degradation data are provided. In this paper, a constant-stress accelerated degradation test model of the Wiener process with random effects is proposed. First, the generalized confidence intervals of the model parameters are developed by constructing generalized pivotal quantities. Second, utilizing the substitution method, the generalized confidence intervals for the reliability function of lifetime, mean time to failure and the generalized prediction intervals for the degradation characteristic at the normal operating condition are also developed. Simulation studies are conducted to investigate the performances of the proposed generalized confidence intervals and prediction intervals. The simulation results reveal that the proposed generalized confidence intervals and prediction intervals work well in terms of the coverage percentage. In particular, a comparative analysis is made with the traditional bootstrap confidence intervals. At last, the proposed procedures are used for a real data analysis.