Residual Life Prediction for a System Subject to Condition Monitoring and Two Failure Modes Abstract—In this paper, we investigate the residual life prediction problem for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example. Keywords—Partially observable system, hidden Markov model, competing risks, residual life prediction. I. I NTRODUCTION R ECENTLY, due to the advances in sensor development, data measurement technology, and computer technology, it became possible to implement effective condition monitoring systems for critical equipment in many companies’ information systems. This information can be utilized for the assessment of the actual condition of the operating equipment without any unwanted disruption or unplanned stopping of the operation, which usually result in a high cost due to lost production. A maintenance strategy referred to as condition-based maintenance (CBM) can then be developed and comparing with the traditional maintenance techniques, CBM reduces the risk of catastrophic system failure as well as the maintenance cost. It is obvious that the collected data carries only partial information about the unknown, hidden state of the equipment and the dimensionality of such data is typically very large, with lots of redundancy, noise, and substantial cross and auto correlation present. Various approaches for processing and modeling of such information have been proposed in the literature which can be generally classified as nonparametric and parametric techniques (see e.g. [1], [2], [3], [4], [5]). Although systems with two failure modes appear in a variety of technical applications, majority of existing CBM models consider only single failure mode. In fact, [6] is the only reference where CBM with multiple failure modes was developed for continuously monitored degrading systems. However, this assumption is no longer valid when the system state is monitored at discrete times, which is the usual practice. Such a drawback of existing models motivates us to consider a CBM model with two modes of failures (competing risks) A.Khalegheil is with the Department of Mechanical & Industrial V.Makis is with the Department of Mechanical & Industrial Engineering, i.e., a catastrophic and degradation failures which arise quite naturally and are of much interest in the reliability area. In this paper, we focus on the application of a parametric technique which can be used to extract useful information for early fault detection and reliability estimation of a technical system subject to both deterioration and sudden failures. The system is subject to condition monitoring and data collection at regular times. We assume that three types of data histories are available: histories that end with observable system failure caused by degradation, histories that end with observable sudden failure, and suspension histories. The evolution of the actual state of the monitored equipment can be modeled in several ways, for example using the proportional hazards model [7], [2], hidden Markov model [8], [4] or hidden semi-Markov model [9], [10]. We assume that the degradation process evolves as a continuous-time homogeneous Markov chain (Z t : t ∈ R + ) with state space Z = {1, 2, 3}, where states 1 and 2 are unobservable, representing the healthy and unhealthy operational states respectively, and state 3 represents the observable failure state. There have been two approaches for a joint parameter estimation of the hidden Markov model using the expectation-maximization (EM) algorithm. The first approach uses the pre-processed observation data directly and applies a state-space representation of the observation process model and Kalman filtering [11], which is computationally very intensive. The second approach focuses on fitting a vector autoregressive model to the pre-processed observation data, then calculating the residuals using the fitted model for the complete data histories and defining the observation process as the residual process. This approach utilizes the results in [12], where it was proved that such residuals are independent and normally distributed, which simplifies the application of EM algorithm for the joint HMM and residual process parameter estimation [13]. In this paper, we develop a new model for a system with two failure modes in Section II. The estimation procedure based on the EM algorithm is developed in Section III, where the observation process is defined as the residual process obtained after data pre-processing and fitting the reference model to the in-control portion of data histories. The formulas for the conditional reliability (RF) and mean residual life (MRL) function are presented in Section IV. The whole procedure is illustrated by an example in Section V, followed by conclusions in Section VI. Akram Khaleghei Ghosheh Balagh, Viliam Makis Engineering, University of Toronto, Toronto, Canada, (e-mail:akhalegh@ mie.utoronto.ca). University of Toronto, Toronto, Canada, (e-mail: makis@mie.utoronto.ca). World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:8, No:6, 2014 955 International Scholarly and Scientific Research & Innovation 8(6) 2014 ISNI:0000000091950263 Open Science Index, Mechanical and Mechatronics Engineering Vol:8, No:6, 2014 publications.waset.org/9998559/pdf