Planning accelerated life tests with multiple sources of random effects

Accelerated life testing (ALT) is a commonly used experiment in industries for assessing a product's lifetime. Planning a proper test with consideration of possible constraints on randomization is important because the prediction accuracy highly depends on the test plan. In this article, an optimal ALT test plan with multiple sources of random effects is demonstrated. Specifically, we consider two types of random effects caused by subsampling and blocking, and the experimental design consists of a crossed experimental factor - supplier, as well as a nested experimental factor - test chamber. The D-optimal ALT test plan is derived via a quasi-likelihood approach. An optimization algorithm with three iterative steps is developed to determine testing stress conditions, chamber assignments, and the number of test units for each testing condition and their supplier sources. The resulting test plans assign test units to chambers such that the effect of stress factor will not confound with the effect of test chamber and a similar number of test units from different suppliers will be required for each test condition.