Optimal Setting of Test Conditions and Allocation of Test Units for Accelerated Degradation Tests with Two Stress Variables

Conducting accelerated degradation tests (ADTs) is an effective way to assess reliability of highly reliable products. In the existing literature, most works deal with planning ADT with a single stress variable; however, the situation of more than one stress variable is commonly seen in engineering practice. To fill the gap, in this article, we provide an analytical approach to address the design issue when two stress variables are present. By using a linear mixed-effects model to describe the accelerated degradation process, we demonstrate that the design problem can be solved by, first, finding the optimal setting of test conditions and allocation of test units for a 'single-variable' case, and then the initial solution is transformed to the test plan for the case of two stress variables. The transformation is done by maintaining the same value of the asymptotic variance of the estimated pth quantile lifetime, along with the consideration of reducing the asymptotic variance of model parameters estimation. We also discuss how to find compromise plans that satisfy practical demands. Finally, the proposed framework is illustrated using a real-world example.