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Mathematical Problems in Engineering
Volume 2012, Article ID 347675, 19 pages
Research Article

Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

1Department of Mathematics, Faculty of Science, Xi'an Jiaotong University, Shaanxi, Xi'an 710049, China
2School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China

Received 10 June 2011; Revised 8 September 2011; Accepted 30 September 2011

Academic Editor: Pedro Ribeiro

Copyright © 2012 Qihong Duan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm.