Mis-specification analysis of the impact of covariates on the diffusion coefficient in Wiener degradation process

Abstract

The diffusion coefficients are often assumed irrelevant to stresses in Wiener degradation process. However, there is evidence that the diffusion coefficients under different accelerated stress levels are different in an accelerated degradation test where higher accelerated stress could lead to larger diffusion. Therefore, in contrast to the existing models in which the diffusion coefficients are assumed as a constant or irrelevant to stress levels, this paper allows both the drift coefficients and the diffusion coefficients to be defined as the functions of accelerated stresses. Then, the consequence of model mis-specification in which the proposed model is wrongly fitted by its special case is analyzed based on Kullback–Leibler distance. In addition, the influence of each degradation parameter on the relative bias and the relative variation of the mean time to failure and 100p th percentage of first hitting time is analyzed by simulation methods. Finally, some important differences between the two models are verified by two case studies.

Keywords:

• Accelerated degradation test
• Diffusion coefficient
• Mis-specification
• Nonlinear Wiener process

Acknowledgments

The authors would like to thank the anonymous reviewers and the associated editor for their constructive comments and useful suggestions on this manuscript.