Approximate parameter estimation and mis-specification analysis of degradation model with asymmetric random effects

Asymmetric distributions such as the skew-normal (SN) distribution have been used for modeling the unit-to-unit variation of the degradation rate of products, and its superiority for model fitting and lifetime estimation has been demonstrated in literature. However, there still exist two issues that need to be further studied. That is, how to simply estimate the parameters of the degradation model with asymmetric random effects and whether the asymmetry or skewness affects the remaining useful life (RUL) prediction. Driven by these two issues, the parameter estimation and RUL prediction of the degradation model with general random effects are first introduced and a two-step maximum likelihood estimation (MLE) method for parameter estimation is proposed, which could greatly simplify the parameter estimation of the degradation model with asymmetric random effects. Then, the SN distribution is used as an example to analyze the second issue regarding the effect of model mis-specification on RUL prediction based on regression models and Wiener processes with different asymmetric random effects in theory. Finally, the parameter estimation and mis-specification analysis of degradation models with other asymmetric random effects are conducted through numerical examples and two case studies. The results demonstrate that the proposed two-step MLE method is satisfactory and the effect of asymmetry on RUL prediction is negligible. Therefore, there is no need to consider the asymmetry of random effects for RUL prediction.