Optimal planning of step-stress accelerated degradation test based on Tweedie exponential dispersion process with random effects

The step stress accelerated degradation test (SSADT) is an effective tool for assessing the reliability of highly reliable products. However, conducting an SSADT is expensive and time consuming, and the obtained SSADT data has an impact on the accuracy of the subsequent product reliability index estimations. Consequently, devising a cost-constrained SSADT plan that yields high-precision reliability estimates poses a significant challenge. This paper focuses on the optimal design of SSADT for the Tweedie exponential dispersion process with random effect (TEDR), a general degradation model capable of describing product heterogeneity. Under given budget and boundary constraints, the optimal sample size, observation frequency and observation times at each stress level are obtained by minimizing the asymptotic variance of the estimated quantile life at normal operating conditions. The sensitivity and stability of the SSADT plan are also studied, and the results indicate the robustness of the optimal plan against slight parameters fluctuations. We use the expectation maximization (EM) algorithm to estimate TEDR parameters and reliability indicators under SSADT, providing a systematic method for obtaining the optimal SSADT plan under budget constraints. The proposed framework is illustrated using the case of LED chips data, showcasing its potential for practical application.