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IMA Journal of Management Mathematics Advance Access published online on July 4, 2005
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpi035
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Article

Modelling the probability assessment of system state prognosis using available condition monitoring information

Wenbin Wang 1*

1 Centre for OR and Applied Statistics, University of Salford, Salford, M5 4WT, UK

* To whom correspondence should be addressed.
Wenbin Wang, E-mail: w.wang{at}salford.ac.uk


  Abstract

This paper reports on a model to assess the current and future states of a monitored system based on measured condition monitoring information to date. The true state of the system is unobservable, but is assumed to be related to the measured condition monitoring information in a stochastic way. We further assume that the transition of the system state follows a time-dependent Markov chain which has only three states, namely good, defective and failed. This assumption effectively defines a two-stage failure process which is widely used in delay time modelling of maintained systems. Three modelling techniques are used to establish the model. First, we use a hidden Markov model to describe the transitions between system states. Second, the transition matrix is established based on the well-known delay time concept. The last one is the use of the filtering technique to construct the relationship between measured condition information and the underlying true state of the system. We also discuss the procedure for model parameter estimation. A numerical example is presented to demonstrate the modelling ideas.

Keywords: system state prognosis; condition monitoring; hidden Markov models; delay time; filtering.
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