Optimal Planning of Step‐Stress Accelerated Degradation Test Based on Tweedie Exponential Dispersion Process With Model Misspecification

The optimal design of step‐stress accelerated degradation tests (SSADT) is important in reliability analysis, and the solved optimal plan often relies on underlying degradation model. However, the degradation model may be mis‐specified. A SSADT design problem under model mis‐specification scenario remains underexplored. In this study, we investigate the effect of model misspecification on the optimal plan when the true model comes from Tweedie exponential dispersion (TED) process with random effect, but is wrongly assumed to be Wiener, Gamma, and inverse Gaussian processes with random effect respectively. We derive the asymptotic variance of mean time‐to‐failure (MTTF) and minimize it under cost constraints to optimize plan. Finally, a numerical example involving LED chip data set is used to illustrate the method's practicality. Results show that, when the mis‐specified model is close to the true model, the corresponding optimal plans and properties under the mis‐specified model are close to those under the true model. In addition, when the mis‐specified model is far from the true model, the corresponding optimal plans are different from those under the true model, and the plans under the mis‐specified model show a certain robustness, which may be dominated by the effects of model mis‐specification.