Optimal design of stress levels in accelerated degradation testing for multivariate linear degradation models

In recent years, more attention has been paid prominently to accelerated degradation testing (ADT) in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years or even decades. In this paper, we propose optimal experimental designs for repeated measures ADTs with competing failure modes that correspond to multiple response components. The marginal degradation paths are expressed using linear mixed effects models. The optimal design is obtained by minimizing the asymptotic variance of the estimator of some quantile of the failure time distribution at the normal use conditions. Numerical examples are introduced to ensure the robustness of the proposed optimal designs and compare their efficiency with standard experimental designs.