Design of accelerated degradation tests for reliability assessment

Abstract

Accelereted degradation tests (ADTs) are widely used in many context for the reliability assessment of products. In this thesis, we develop optimal ADT plans under the assumptions of destructive testing and the simple constant rate relationship between the degradation of product performance and time. Specifically, we determine 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 qth quantile of the lifetime distribution 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. Also, the developed optimal ADT plans are compared to the corresponding optimal accelerated life test (ALT) plans in terms of the asymptotic efficiency in estimating the qth quantile and of the robustness to the mis-specifications of failure probabilities. Computational results show that the ADT provides a more precise estimator than the ALT, especially when the failure probabilities are small. As long as the robustness of a test plan to the departures of the guessed failure probabilities from their true values is concerned, neither plan completely dominates the other. Finally, we develop reliability acceptance sampling plans (RASPs) based on the ADT such that the producer and the consumer risks are satisfied.