Parameter estimation in a condition-based maintenance model

• Published in: Statistics & probability letters Vol. 80; no. 21; pp. 1633 - 1639
• Main Authors: Kim, Michael Jong, Makis, Viliam, Jiang, Rui
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2010; Elsevier
• Series: Statistics & Probability Letters
• Subjects: EM algorithm; Exact sciences and technology; General topics; Hidden Markov modeling; Inference from stochastic processes; time series analysis; Markov processes; Mathematics; Parameter estimation; Parameter estimation Partially observable failing systems Hidden Markov modeling Vector time series EM algorithm; Partially observable failing systems; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Vector time series; Parameter estimation; Vector time series; Partially observable failing systems; Hidden Markov modeling; EM algorithm; Markov process; Information system; Probability theory; Time series; Continuous time; Statistical estimation; Statistical method; Pseudolikelihood; Discrete time; Maximum likelihood; Likelihood function; Autoregressive processes
• DOI: 10.1016/j.spl.2010.07.002
• ISSN: 0167-7152

A parameter estimation problem for a condition-based maintenance model is considered. We model a failing system that can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is assumed to follow a hidden, three-state continuous time Markov process. Vector autoregressive data are obtained through condition monitoring at discrete time points, which gives partial information about the unobservable system state. Two kinds of data histories are considered: histories that end with observable system failure and histories that end when the system is suspended from operation but has not failed. Maximum likelihood estimates of the model parameters are obtained using the EM algorithm and a closed form expression for the pseudo-likelihood function is derived. Numerical results are provided which illustrate the estimation procedure.