Abstract:We consider a partially observable degrading system subject to condition monitoring and random failure. The system's condition is categorized into one of three states: a healthy state, a warning state, and a failure state. Only the failure state is observable. While the system is operational, vector data that is stochastically related to the system state is obtained through condition monitoring at regular sampling epochs. The state process evolution follows a hidden semi-Markov model (HSMM) and Erlang distribution is used for modeling the system's sojourn time in each of its operational states. The Expectation-maximization (EM) algorithm is applied to estimate the state and observation parameters of the HSMM. Explicit formulas for several important quantities for the system residual life estimation such as 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. Numerical examples are presented to demonstrate the applicability of the estimation procedure and failure prediction method. A comparison results with hidden Markov modeling are provided to illustrate the effectiveness of the proposed model.

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.

In “Optimal Control of Partially Observable Semi-Markovian Failing Systems: An Analysis using a Phase Methodology,” Khaleghei and Kim study a maintenance control problem a as partially observable semi-Markov decision process (POSMDP), a problem class that is typically computationally intractable and not amenable to structural analysis. The authors develop a new approach based on a phase methodology where the idea is to view the intractable POSMDP as the limiting problem of a sequence of tractable POMDPs. They show that the optimal control policy can be represented as a control limit policy which monitors the estimated conditional reliability at each decision epoch, and, by exploiting this structure, an efficient computational approach to solve for the optimal control limit and corresponding optimal value is developed.

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.