Risk evaluation for deteriorating systems with accuracy analysis of parameter estimation

Risk analysis, which is a useful methodology to evaluate the performance of systems, can provide important information for maintenance decision and ensure stable running of the system. As a score function of the occurrence, severity and detection of a failure, risk priority number is the most common risk analysis approach. For degrading systems, the probability of failure occurrence could be obtained by modeling the degradation path, and the severity of failure could be quantified through engineering experience. Generally, the accuracy of the model is affected by the number of training data reflecting the detection. In this paper, we focus on statistical data driven approaches, which rely on the degradation data and statistical process model to describe the degradation path. First of all, we discuss the relationships between the accuracy of parameter estimation with likelihood function as well as the corresponding information entropy, based on probability theory and information theory. Then relative entropy indicating the distance between two distributions is utilized to evaluate the accuracy of parameter estimation, i.e. the degree of detection. Moreover, the risk value can be derived, because the probability of failure can be evaluated via modeling the degradation path. Finally, a numerical study is provided to illustrate the rationality and advantage of the proposed method over the traditional one.