Modeling, estimation, and control of partially observable failing systems using phase method

Recently, due to the advances in data measurement and computer technology, it has become possible to implement effective condition monitoring (CM) systems for critical equipment which increase plant productivity. The objective is to utilize the information obtained from CM for the assessment of the actual condition of the operating equipment without any unwanted interruption. In most applications, the collected CM data involves uncertainty and relates probabilistically to the exact state of the system. Most previous maintenance and reliability models in the literature do not incorporate CM information for decision making or assume that the CM system provide full information about the system true state, which often results in poor failure prediction. This research presents a new framework for predicting failures of a partially observable deteriorating system using Bayesian control techniques. The system can be in one of three-state: healthy state, an unhealthy or deteriorated state, and a failure state. Only the failure state is assumed to be observable. A vector autoregressive model is fitted to the observation process and residuals are then calculated using the fitted model, which are indicative of system deterioration. The state deterioration evolution is modeled using three-state hidden Markov model and hidden semi-Markov model. We develop optimal maintenance policy using multivariate Bayesian control approach for developed models. The posterior probability that the process operates in an unhealthy condition is updated using Bayes' rule at each sampling epoch and used for decision making. When the posterior probability exceeds a control limit, the system is stopped and full inspection is performed which reveals the true system condition. Preventive maintenance is then carried out if the system is in the unhealthy state. The objective is to find the optimal maintenance policy minimizing the long-run expected average cost. We solve the problem in the semi-Markov decision process framework. The model parameters are estimated and explicit formulas for several important quantities for the system residual life estimation are derived as functions of a posterior probability statistic. The methodologies are illustrated using simulated and the real data.

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