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

Abstract

Statistically optimal and compromise step-stress accelerated degradation test (ADT) plans are developed under the assumption that the degradation characteristic follows a Wiener process. Compromise plans are provided for the case where the experimenter wants to check the validity of the assumed stress-parameter relationship. Two and three step-stress levels are respectively considered in the statistically optimal and compromise ADT plans. For both types of plans, step-stress level(s) and stress level change time(s) are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized. A distinctive feature of the proposed ADT plans is that the stress level can be changed not only at a measurement time but also between two successive measurement times. This feature allows a more general formulation of the two-step-stress ADT planning problem and more flexible three-step-stress compromise ADT plans. Computational results show that in a statistically optimal ADT plan (with two-step-stress levels) the stress change time always coincides with a measurement time. On the other hand, for a compromise plan the stress level sometimes needs to be changed between two successive measurement times to satisfy certain planning requirements. Using an example, the above planning methods are illustrated, the sensitivity of a plan with respect to the uncertainty in the pre-estimate of a model parameter is assessed, and the proposed step-stress ADTs are compared with the constant-stress ADTs and conventional step-stress ADTs in terms of the sample size and/or total testing time.