Reliability estimation of a system subject to condition monitoring with two dependent failure modes

Abstract

A new competing risk model is proposed to calculate the conditional mean residual life (CMRL) and conditional reliability function (CRF) of a system subject to two dependent failure modes namely, degradation failure and catastrophic failure. The degradation process can be represented by a three state continuous-time stochastic process having a healthy state, a warning state, and a failure state. The system is subject to condition monitoring at regular sampling times providing partial information about the system working state and only the failure state is observable. To model the dependency between two failure modes, it is assumed that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follows Marshal-Olkin Bivariate Exponential distribution. Expectation-Maximization algorithm is developed to estimate the model's parameters and the explicit formulas for the CRF and CMRL are derived in terms of the posterior probability that the system is in the warning state. A comparison with a previously published model is provided to illustrate the effectiveness of the proposed model using real data.

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

“…The occurrence time of catastrophic failure and the sojourn time of the system in the healthy state are denoted by ξ 1 and τ 0 , respectively. Considering the dependence of degradation failure and catastrophic failure, for t ≥ 0, w ≥ 0, the joint survival function of random variables ( ξ 1 , τ 0 ) is given as follows: where ( ξ 1 , τ 0 ) follows the Marshall–Olkin's BED, which is denoted by ( ξ 1 , τ 0 )~ BED ( λ 1 , λ 2 , λ 3 ).…”

“…The approaches using condition monitoring information for system degradation modeling with competing failure modes usually include fuzzy physics‐based model, random shock models, Wiener process, and Markov models . Among these models, Markov models are applied most extensively in the areas of reliability analysis and optimal maintenance decision‐making.…”

“…However, the catastrophic failure may occur at any time. A recent study has proved that in CBM, it is sufficient to consider two unobservable operational states (healthy and unhealthy states) and one observable state (failure state) using real condition monitoring data to implement fault detection and residual life estimation . In light of the above considerations, we use a three‐state HMM to describe the degradation process of the gear system.…”

“…Using availability maximization as the criterion, Jiang et al investigated the optimal Bayesian control scheme for gear shaft fault detection considering a single failure mode. Although Khaleghei and Makis developed a three‐state HMM with two dependent failure modes to estimate the reliability of a system, no maintenance policy was considered in their paper. The limitations of the existing optimization models motivate us to consider an optimal maintenance model with multiple dependent failure modes.…”

Estimation on Reliability Models of Bearing Failure Data

“…To solve the real-time online reliability problems, Hong and Meeker [20] proposed an intelligent reliability estimation method based on dynamic state information changes, which brought much convenience to timely judge the dynamic running state of workpiece. Khaleghei and Makis [21] proposed a new competing risk model to calculate the conditional mean residual life and conditional reliability function of a system subject to two dependent failure modes, namely, degradation failure and catastrophic failure. In order to ensure that the classifier can correctly inspect the system failure information, Hwang and Lee [22] presented a new approach to overcome class imbalance problem and human factor influence by using classification technique, thus speedily and effectively implementing system reliability estimation.…”