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Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations

Part of: Operations research and management science Stochastic processes 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 M5S 3G8, Canada.
∗∗ Email address: makis@mie.utoronto.ca
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Abstract

We consider a failure-prone system operating in continuous time. Condition monitoring is conducted at discrete time epochs. The state of the system is assumed to evolve as a continuous-time Markov process with a finite state space. The observation process with continuous-range values is stochastically related to the state process, which, except for the failure state, is unobservable. Combining the failure information and the condition monitoring information, we derive a general recursive filter, and, as special cases, we obtain recursive formulae for the state estimation and other quantities of interest. Updated parameter estimates are obtained using the expectation-maximization (EM) algorithm. Some practical prediction problems are discussed and finally an illustrative example is given using a real dataset.

Keywords

Partially 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 36 , Issue 4 , December 2004 , pp. 1212 - 1230
Copyright
Copyright © Applied Probability Trust 2004 

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