Optimal design of accelerated degradation tests based on Wiener process models

Abstract

Optimal accelerated degradation test (ADT) plans are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Unlike the previous works on planning ADTs based on stochastic process models, this article determines the test stress levels and the proportion of test units allocated to each stress level such that the asymptotic variance of the maximum-likelihood estimator of the qth quantile of the lifetime distribution at the use condition is minimized. In addition, compromise plans are also developed for checking the validity of the relationship between the model parameters and the stress variable. Finally, using an example, sensitivity analysis procedures are presented for evaluating the robustness of optimal and compromise plans against the uncertainty in the pre-estimated parameter value, and the importance of optimally determining test stress levels and the proportion of units allocated to each stress level are illustrated.