Mis-specification analysis of the degradation model based on Wiener process and random coefficient regression model

Various types of Wiener processes have been studied quite extensively to apply for highly reliable products’ degradation modeling. The simple random coefficient regression (RCR) model also demonstrates a relatively robust ability in predicting lifetime and remaining useful life (RUL). Therefore, this paper investigates the differences between the RCR model and the Wiener process in terms of lifetime estimation and RUL prediction, providing a reference for selecting an appropriate model. Specifically, considering the importance of parameters estimation for model mis-specification analysis, the analytical expressions of unbiased parameters estimation based on RCR models are first derived. Then, based on this, the modeling differences between the RCR model and the Wiener process under the same degradation data are analyzed, and the probability density function (PDF) distributions of estimated lifetime and predicted RUL are provided to illustrate the impact of model mis-specification specification. Finally, results from several numerical examples and case studies show that under the same degradation data with up and down fluctuations, the results predicted by the Wiener process are more conservative than those of the RCR model, making it suitable for high-risk areas, while the RCR model is suitable for cost-sensitive applications.