Degradation data analysis based on gamma process with random effects

This paper focuses on investigating the Gamma degradation model with random effects. A generalized p-value procedure is proposed to test whether there exist some heterogeneities among the degradation processes of different units. Using the Cornish-Fisher expansion, an approximate confidence interval (CI) is obtained for the shape parameter. The generalized confidence intervals (GCIs) are derived for model parameters and commonly used reliability metrics (e.g., the quantile, the reliability function of the lifetime) based on the generalized pivotal quantity method. Those inference procedures are also extended to the accelerated degradation case. The performances of the proposed GCIs are assessed by Monte Carlo simulations. In the simulation, we compared our methods with the Wald CIs and bootstrap-p CIs under moderate and large sample sizes. It is found that the performance of the GCI procedures is better than the Wald CIs and bootstrap-p CIs in terms of coverage probabilities. Finally, the proposed procedures are illustrated by two examples.