Premium
Maximum Likelihood Estimation for a Hidden Semi‐Markov Model with Multivariate Observations
Author(s) -
Jiang Rui,
Kim Michael Jong,
Makis Viliam
Publication year - 2012
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1418
Subject(s) - multivariate statistics , maximum likelihood , statistics , hidden markov model , markov model , markov chain , estimation , mathematics , multivariate analysis , econometrics , estimation theory , expectation–maximization algorithm , computer science , artificial intelligence , engineering , systems engineering
In this paper, a parameter estimation procedure for a condition‐based maintenance model under partial observations is presented. The deterioration process of the partially observable system is modeled as a continuous‐time homogeneous semi‐Markov process. The system can be in a healthy or unhealthy operational state, or in a failure state, and the sojourn time in the operational state follows a phase‐type distribution. Only the failure state is observable, whereas operational states are unobservable. Vector observations that are stochastically related to the system state are collected at equidistant sampling times. The objective is to determine maximum likelihood estimates of the model parameters using the Expectation–Maximization (EM) algorithm. We derive explicit formulae for both the pseudo likelihood function and the parameter updates in each iteration of the EM algorithm. A numerical example is developed to illustrate the efficiency of the estimation procedure. Copyright © 2012 John Wiley & Sons, Ltd.