Planning Dual-Stress Accelerated Degradation Tests with Random-Effects Wiener Process Models

In industry, accelerated degradation tests (ADTs) are widely used to efficiently assess products’ reliability. A common feature observed in many ADTs is unit-to-unit variability, which includes random initial degradation levels and degradation rates, as well as the potentially strong correlation between these two factors – often referred to as the “initiation-growth” correlation. Motivated by a real-world application in optical media, this article investigates the design of ADTs involving single or dual stress variables within a Wiener process framework that accounts for these random effects. Optimum test plans, in terms of test condition settings and sample allocation, are determined by minimizing the asymptotic variance of the estimated pth quantile lifetime under the normal use condition. For dual-stress ADTs, we propose a splitting strategy that generates statistically equivalent three-point nondegenerate plans by decomposing the lower-stress point of a two-point degenerate plan along an iso-stress direction while preserving its weighted centroid. This yields infinitely many globally C-optimal plans, among which the boundary-extreme split attains D-optimality within this class. To address potential deviations from model assumptions, we explore compromise plans that enhance robustness. Additionally, we investigate a strategic allocation rule that assigns units to test conditions based on the ranked initial degradation levels. Comparative analysis with the conventional random allocation rule reveals that this approach does not consistently yield superior results. Case studies drawn from the motivating application demonstrate the performance and practical value of the proposed methodology. Detailed proofs and additional numerical results are available in the online supplementary materials.