Mis-specification Analyses of Nonlinear Wiener Process-based Degradation Models

Abstract

For some highly reliable products, degradation data have been studied quite extensively to evaluate their reliability characteristics. However, the accuracy of evaluation results depends strongly on the suitability of the proposed degradation model for capturing the degradation over time. If the degradation model is mis-specified, it may result in inaccurate results. In this work, we focus on the issue of model mis-specification between nonlinear Wiener process-based degradation models in which both the product-to-product variability and the temporal uncertainty of the degradation can be considered simultaneously with the nonlinearity in degradation paths. Specifically, a generalized Wiener process-based degradation model is wrongly fitted by its two limiting cases. The effects of model mis-specification in such situations on the MTTF (mean-time-to-failure) of the product are measured with the relative bias and the relative variability. Results from a numerical example concerning fatigue cracks show that the effect of mis-specification is serious under some parameter settings, i.e., the relative bias departs from 0, and the relative variability significantly departs from 1, if the generalized Wiener degradation process is wrongly assumed to be its limiting cases.

Keywords:

• Degradation model
• Mean-time-to-failure
• Model mis-specification
• Nonlinear Wiener process.

Mathematics Subject Classification:

• Primary 62-xx; Secondary 62Mxx