Data Analysis of Step-Stress Accelerated Life Test with Random Group Effects under Weibull Distribution

Step-stress accelerating life test (SSALT), aiming to predict the failure behavior under use condition by the data collected from elevated test setting, is implemented to specimen with time-varying stress levels. Typical testing protocols in SSALT, such as subsampling, cannot guarantee complete randomization and thus result in correlated observations among groups. To consider the random effects from the group-to-group variation, we build a nonlinear mixed effect model (NLMM) with the assumption of Weibull distribution for life time data analysis from SSALT. Both maximum likelihood estimation (MLE) and Bayesian inference are introduced for the estimation and prediction of model parameters as well as other statistics of interest. Gauss–Hermite (G-H) quadrature is used to obtain an accurate approximation of the likelihood for observations, and different priors of model parameters are applied in Bayesian analysis. A comprehensive simulation study and an analysis for a real data set are conducted to justify the proposed method, suggesting that the incorporation of the random effect from the underlying experimental routine ensures a more solid and practical conclusion when the heterogeneous group effect is statistically significant.