Abstract
Accelerated degradation tests (ADTs) are widely used to assess the lifetime information (e.g., the p-quantile of the lifetime distribution) of highly reliable products when their quality characteristics (QCs) are closely related to reliability. In practical applications, gamma and inverse Gaussian degradation models are well-known to describe the degradation paths which reveal monotone increasing patterns. Due to possessing very similar degradation paths, these two models are often mis-specified with each other. Therefore, their misspecification analysis shall be an interesting research topic. In this study, we apply White (1982) to address their misspecification effects on the p-quantile of the lifetime distribution. Specifically, in the large sample, we first derive the asymptotic distribution of quasi-maximum likelihood estimation (QMLE) of the p-quantile when the true model is a gamma (inverse Gaussian) accelerated degradation model, but was mis-specified as an inverse Gaussian (gamma) accelerated degradation model. Their misspecification effects on relative bias (RB) and relative variability (RV) are also addressed analytically. Next, we use a modified Device-B dataset to illustrate the misspecification effects between these two degradation models. The results demonstrate that the RBs are not serious for both dual misspecification problems. However, their RVs are not negligible. We also conduct a simulation study to address the performances of misspecification risks. The results demonstrate that adopting inverse Gaussian model has a better performance on the expected mean square error (EMSE). In addition, the RB and RV values for the case of small sample are very similar to that of the case of large sample. Finally, we also propose a simple way to determine the settings of measurement times for both low and high stresses. The results demonstrates that the low-stress (high-stress) level with more (less) measurement times is a good strategy for implementing an ADT plan.