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Parameter estimation for partially observable systems subject to random failure


Correspondence to: Viliam Makis, Mechanical and Ind. Eng., University of Toronto Toronto, ON M5S 3G8, Canada.



In this paper, we present a parameter estimation procedure for a condition-based maintenance model under partial observations. Systems can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is driven by a continuous time homogeneous Markov chain and the system state is unobservable, except the failure state. Vector information that is stochastically related to the system state is obtained through condition monitoring at equidistant sampling times. Two types of data histories are available — data histories that end with observable failure, and censored data histories that end when the system has been suspended from operation but has not failed. The state and observation processes are modeled in the hidden Markov framework and the model parameters are estimated using the expectation–maximization algorithm. We show that both the pseudolikelihood function and the parameter updates in each iteration of the expectation–maximization algorithm have explicit formulas. A numerical example is developed using real multivariate spectrometric oil data coming from the failing transmission units of 240-ton heavy hauler trucks used in the Athabasca oil sands of Alberta, Canada. Copyright © 2012 John Wiley & Sons, Ltd.