Mechanism equivalence analysis for accelerated degradation tests based on tweedie exponential dispersion process

Mechanism equivalence analysis, focusing on the underlying quantitative relationship between degradation model parameters under different stress levels when the accelerated failure mechanism remains unchanged, has been developed and adopted widely in accelerated degradation tests (ADTs) over recent years. For a specific degradation process, the mechanism equivalence conditions can be derived based on the acceleration factor invariant principle and further utilized to test whether the accelerated failure mechanism remains unchanged or not under different stress levels. In this paper, a unified form of the mechanism equivalence conditions for commonly-used stochastic process models is derived based on Tweedie exponential dispersion process. The unified form can cover the conditions of Wiener, Gamma and inverse Gaussian processes, etc. Based on this, a complete procedure for mechanism equivalence test of ADT is proposed through the joint application of normality test and parameter hypothesis tests. In this way, the availability of the ADT data can be distinguished before using them for lifetime prediction of products. In addition, the effects caused by degradation model mis-specification and ADT data misuse are further analyzed from the perspective of relative error. A simulation example and two real-world case studies are used to demonstrate the effectiveness of the proposed methods.