A nonlinear Wiener process degradation model with autoregressive errors

Degradation information reflecting the product or system health state plays an important role in assessing reliability and making maintenance schedule. Since degradation inspections are usually compounded and contaminated by measurement errors in real applications, the conventional Wiener process with identically distributed independent Gaussian error is usually adopted. However, in many situations, autocorrelation may probably exist among the measurement errors at sequential test points because of cyclic changes or modeling errors, especially when the time intervals are relatively short. Motivated by this practical issue, a Wiener process degradation model with one-order autoregressive (AR(1)) measurement errors is proposed for degradation analysis. Explicit forms of the probability distribution function (PDF), the cumulative distribution function (CDF) and the corresponding mean time to failure (MTTF) are derived based on the concept of first hitting time (FHT). Furthermore, maximum likelihood estimations (MLE) of unknown parameters are derived. The effects of model mis-specification regarding the estimation of MTTF are also discussed. Finally, a comprehensive simulation study and two practical applications are given to demonstrate the necessity and efficiency of the proposed model.