Reliability estimation of a production system subject to condition monitoring with two modes of failures

In this paper, we present a new fault prediction model for a partially observable production system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The degradation process is described by a three states hidden Markov model(HMM). It is assumed that the time to sudden failure is dependent on system operating state. The parameter estimation procedure based on the Expectation-Maximization(EM) algorithm is developed. Explicit formulas for the conditional reliability function and the mean residual life are derived in terms of the posterior probability that the system is in the warning state. The method is illustrated using simulated data. The effectiveness of the proposed HMM to predict failures is then compared with the performance of the previously published HM model.