基于逆高斯退化模型的错误指定分析

摘要

针对目前随机过程退化模型错误指定研究较少,且主要集中在线性模型中的现状,研究了逆高斯过程(inverse Gaussian,IG)的两类错误指定:不含随机效应情况下非平稳IG过程被错误指定为非线性Wiener过程,以及含随机效应IG过程被错误指定为简单IG过程.基于伪最大似然估计近似正态性理论获得了这两种情形下伪平均失效前时间(mean-time-to-failure,MTTF)估计的分布特征,并以某合金疲劳裂纹数据为例,分析比较了模型错误指定对MTTF的影响.结果还显示,在特定参数设置或样本数、观测次数组合设置下,模型错误指定将对MTTF的估计带来较大影响,这在工程实践中具有一定参考价值.%The mis-specification effects of stochastic process-based degradation models are rarely studied and mainly focus on linear models.This paper investigates two types of mis-specification in inverse Gaussian (IG) processes, that is, a non-stationary IG process without random effects which is wrongly assumed to be a nonlinear Wiener process without random effects, and an IG process with a random effect which is wrongly assumed to be a simple IG process.In such situations, the distribution characteristics of quasi maximum likelihood estimation (QMLE) of the mean-time-to-failure (MTTF) are derived according to the theory of QMLE asymptotic normality.Through a case study about fatigue-crack-growth data, the effects of the corresponding model's misspecification on the MTTFs are compared and analyzed.The results also show that the effects of mis-specification become large under some settings of parameters, or combinations of the number of the sample size and measurements, which can be used as references to engineering applications.