Advances in Applied Probability

Recursive filters for a partially observable system subject to random failure

Daming Lin and Viliam Makis

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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.

Article information

Adv. in Appl. Probab. Volume 35, Number 1 (2003), 207-227.

First available in Project Euclid: 27 February 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

Partly observable system continuous-discrete model change of measure recursive filter parameter estimation condition-based maintenance


Lin, Daming; Makis, Viliam. Recursive filters for a partially observable system subject to random failure. Adv. in Appl. Probab. 35 (2003), no. 1, 207--227. doi:10.1239/aap/1046366106.

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