Optimal Two-Variable Accelerated Degradation Test Plan for Gamma Degradation Processes

Abstract

An accelerated degradation test (ADT) can be used to assess the reliability of highly reliable products by using degradation information. In this study, to exhibit a monotone increasing pattern, the gamma process is used to model the degradation of a product subject to a constant-stress ADT of two loadings. Maximum likelihood estimates (MLEs) of the parameters of the ADT model were obtained. Given a budget for the total cost, an optimal ADT procedure was established to minimize the asymptotic variance of the MLE of the mean time to failure of a product, and the sample size and termination time of each run of the ADT at a constant measurement frequency were determined. An algorithm is provided to achieve an optimal ADT plan. An extensive Monte Carlo simulation was implemented to evaluate the sensitivity of the MLE variations to the sample size. A lumen degradation data set of light emitting diodes is presented to illustrate the proposed method.