Planning of Accelerated Life Tests With Dependent Failure Modes Based on a Gamma Frailty Model

Abstract

Accelerated life tests (ALT) provide timely information on product reliability. As product complexity increases, ALT often generate multiple dependent failure modes. However, the planning of an ALT with dependent failure modes has not been well studied in the literature. This article investigates the statistical modeling and planning of ALT with multiple dependent failure modes. An ALT model is constructed. Associated with each failure mode there is a latent lifetime described by a log-location-scale distribution, and the statistical dependence between different failure modes is described by a Gamma frailty model. The proposed model incorporates the ALT model with independent failure modes as a special limiting case. We obtain the c-optimal test plans by minimizing the large-sample approximate variance of the maximum likelihood estimator of a certain life quantile at use condition. The method is illustrated by developing ALT plans for field-effect transistors with competing gate oxide breakdown. A sensitivity analysis is performed to investigate the robustness of the optimal ALT plan against misspecification of model parameter values. This article has supplementary materials that are available online.