Bayesian Methods for Planning Accelerated Repeated Measures Degradation Tests

Accelerated repeated measures degradation tests are often used to assess product or component reliability when there would be few or even no failures during a traditional life test. Such tests are used to estimate the failure-time distributions of highly reliable items in applications where it is possible to take repeated measures of some appropriate degradation measure. When engineers have valid prior information about failure mechanisms, it is important that such information be used in inference and test planning. Bayesian methods provide a vehicle for doing this. This article describes methods for selecting a Bayesian repeated measures accelerated degradation test plan when the degradation and acceleration model is linear in the parameters. A Bayesian criterion based on estimation precision of the failure-time quantile at use conditions is selected for finding optimum test plans. We use a large-sample approximation for the posterior distribution to simplify the planning criterion. The general equivalence theorem is used to check for global optimality of the optimum test plan. We also discuss how to find a compromise test plan that satisfies practical constraints while still providing good statistical properties.