Filtering and M-ary Detection in a Minimal Repair Maintenance Model

Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


An age-dependent repair model is considered in this paper. The notion of the “age” of the product and the degree of repair are used to define the virtual age of the product. Two problems are considered in this paper. In the first problem, the degree of repair is a stochastic process and is allowed to switch between a finite number of values due to various phenomena. Switching is assumed to happen according to the jumps of a homogeneous, finite-state Markov chain. We use hidden Markov models (HMM) to develop a recursion to estimate the conditional probability distribution of the degree of repair process. We also use the Expectation-maximization (EM) algorithm to update optimally the probability transitions of this process. In the second problem, the degree of repair is a random variable and belongs to a set of hypotheses hypothesis. At each epoch \(n,\) a list of \(M\) candidate models is available and the optimal one is chosen.


Markov Chain Probability Measure Hide Markov Model Transition Probability Matrix Output Sequence 


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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSultan Qaboos UniversityMuscatSultanate of Oman
  2. 2.Sobey School of BusinessSaint Mary’s UniversityHalifaxCanada
  3. 3.School of Business AdministrationDalhousie UniversityHalifaxCanada

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