Optimal step stress accelerated degradation tests with the bivariate inverse Gaussian process

Abstract

Step‐stress accelerated degradation test (SSADT) has become a prevailing approach to lifetime assessment for highly reliable products. In practice, many products suffer from multiple degradation processes that significantly contribute to failures. In this paper, we investigate the optimal SSADT plans for products subject to two dependent degradation characteristics modeled by a bivariate inverse Gaussian process. The drift parameter of each process is assumed to be influenced by a common stress factor. A bivariate Birnbaum‐Saunders (BVBS)‐type distribution is employed to approximate the lifetime distribution and facilitate the derivation of the objective function. The optimal plans are prescribed under three common optimality criteria in the presence of constraints on test units and inspections. A revisited example of fatigue crack is then presented to demonstrate the proposed methods. Finally, the sensitivity of the SSADT plans is studied, and the results exhibit fair robustness of the optimal plans.