Optimal design of accelerated degradation tests for estimating mean lifetime at the use condition

Abstract

In an accelerated degradation test, higher-than-normal stress levels are employed to hasten the degradation of product performance, and then the observed degradation data are used to estimate various reliability-related quantities at the use (normal) condition. In this paper, optimal accelerated degradation test plans are developed under the assumptions of destructive testing and the simple constant rate relationship between the stress and the product performance. Specifically, the paper determines the stress levels, the proportion of test units allocated to each stress level, and the measurement times such that the asymptotic variance of the maximum likelihood estimator of the mean lifetime at the use condition is minimized. The optimization problem is formulated as a constrained nonlinear program, and exact optimal solutions are obtained for various cases. Sensitivity analysis and sample size determination procedures are also illustrated with an example.