A Bayesian Approach to Condition Monitoring with Imperfect Inspections

Degradation is a common phenomenon for many products. Due to a variety of reasons, the degradation rates of units from the same population are often heterogeneous. In addition, when the degradation process is monitored using dedicated sensors, the measurements are often inaccurate due to various noisy factors. To account for the heterogeneous degradation rate and the non-negligible measurement errors, we model the degradation observations using a random-effects Wiener process with measurement errors. Under the model, direct estimation of current degradation and prediction of future degradation are difficult. We thus develop a filtering algorithm that recursively estimates the joint distribution of the degradation rate and the current degradation levels. Based on the estimates, the distribution of the remaining useful life can be timely predicted. Our method is both computational efficient and storage efficient. Its effectiveness is demonstrated through simulation and real data.