Optimal design of ramp-stress accelerated degradation tests based on the Wiener process

Abstract

Ramp-stress accelerated degradation test (ADT) plans are developed under the assumption that the degradation characteristic follows a Wiener process. A ramp-stress (RS) test has an advantage over a constant-stress (CS) or step-stress (SS) test in that the difficulty of choosing appropriate stress levels in the latter can be alleviated. In addition, RS test plans could be more efficient than CS or SS test plans in terms of the test time or the number of test units. Optimal and compromise RSADT plans are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution under the normal use condition is minimized. The above planning methods are illustrated using a numerical example, and a sensitivity analysis procedure for assessing the robustness of the proposed test plan to the uncertainty in the pre-estimate of model parameters is provided.