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Recursive filters for a partially observable system subject to random failure

Part of: Stochastic processes Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

Daming Lin  and
Viliam Makis
Daming Lin*
Affiliation:
University of Toronto
Viliam Makis*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8.
∗∗ Email address: makis@mie.utoronto.ca
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Abstract

We consider a failure-prone system which operates in continuous time and is subject to condition monitoring at discrete time epochs. It is assumed that the state of the system evolves as a continuous-time Markov process with a finite state space. The observation process is stochastically related to the state process which is unobservable, except for the failure state. Combining the failure information and the information obtained from condition monitoring, and using the change of measure approach, we derive a general recursive filter, and, as special cases, we obtain recursive formulae for the state estimation and other quantities of interest. Up-dated parameter estimates are obtained using the EM algorithm. Some practical prediction problems are discussed and an illustrative example is given using a real dataset.

Keywords

Partly observable systemcontinuous-discrete modelchange of measurerecursive filterparameter estimationcondition-based maintenance

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60G35: Signal detection and filtering 90B25: Reliability, availability, maintenance, inspection
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 1 , March 2003 , pp. 207 - 227
Copyright
Copyright © Applied Probability Trust 2003 

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