Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2012, Article ID 675830, 5 pages
Research Article

Uniqueness of Maximum Likelihood Estimators for a Backup System in a Condition-Based Maintenance

Department of Statistics, School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi, Xi’an 710049, China

Received 14 May 2012; Revised 9 November 2012; Accepted 9 November 2012

Academic Editor: Tadashi Dohi

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.


A parameter estimation problem for a backup system in a condition-based maintenance is considered. We model a backup system by a hidden, three-state continuous time Markov process. Data are obtained through condition monitoring at discrete time points. Maximum likelihood estimates of the model parameters are obtained using the EM algorithm. We establish conditions under which there is no more than one limitation in the parameter space for any sequence derived by the EM algorithm.