Inference for constant-stress accelerated degradation test based on Gamma process

Abstract

• A Gamma accelerated degradation model based on the principle of degradation mechanism invariance is proposed. • The existence of the maximum likelihood estimate of the parameters of the proposed model is proved. • The approximate confidence interval for the shape parameter based on Cornish–Fisher expansion is derived. • The generalized confidence intervals for other model parameters and some important quantities are developed. This paper proposes a Gamma constant-stress accelerated degradation model based on the principle of the degradation mechanism invariance. The maximum likelihood estimators of the parameters of the proposed model are derived. Based on Cornish–Fisher expansion, the approximate confidence interval for the shape parameter of the Gamma degradation process is developed. Since it is difficult to obtain the exact confidence intervals for other model parameters and some quantities such as the mean degradation in unit time, the quantile and the reliability function of the lifetime at the normal stress level, the generalized confidence intervals for these quantities are proposed. The percentiles of the proposed generalized pivotal quantities can be obtained by the simulation. The performances of the proposed confidence intervals are evaluated by the Monte Carlo simulation method. In the simulation study, the proposed confidence intervals are compared with the Wald and the bootstrap- p confidence intervals. The simulation results show that the proposed confidence intervals outperform the Wald and the bootstrap- p confidence intervals in terms of the coverage percentage. Finally, a real example is used to illustrate the proposed procedures.