Degradation-Based State Reliability Modeling for Components or Systems With Multiple Monitoring Positions

Engineering components or systems may have multiple monitoring positions for the degradation observations of single or multiple performance characteristics. For the reliability analysis with multiple degradation processes, the existing works are generally based on the binary-state degradation model and the Copula method, where the component or system survives only if every single monitoring position survives. This article develops a degradation-based continuous multistate reliability model through the definition of the state function, where the component or system state is determined by the states of all the monitoring positions. Furthermore, two reliability analysis frameworks of components or systems with multiple monitoring positions are given: k-out-of-n reliability framework and importance reliability framework. The proposed method not only casts off the binary-state constraint for the degradation modeling, but also gives a new way to analyze the component or system reliability in the case of multiple degradation processes, which are monitored in multiple monitoring positions. A numerical case and a practical case about the train wheel tread are given to demonstrate the availability and the possible advantages of the proposed model.

I. Introduction

Traditional reliability theories mainly concentrate on the binary-state reliability modeling, in which the system and each component are assumed to be either in the working state or in the failure state. In most reliability studies based on the performance degradation, researchers were devoted to the derivation of the lifetime distribution when the reliability is defined as , where is modeled by a stochastic process and is a critical threshold level. However, such a binary-state reliability definition is inapplicable for many real-world components or systems, which have a range of levels of performance [1]. The levels vary from the perfect functioning to complete failure, which means that there are some partial working states or partial failure states. For example, the power of a solar cell may degrade below a certain threshold with time, but it can still serve the solar module within its residual ability. The extent of the wear caused by the aging degradation process in a bearing shell may extend up to a critical alarm threshold, but it can still work at some danger levels.