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

In: Replacement Models with Minimal Repair

Author

Listed:
  • Lakhdar Aggoun

    (Sultan Qaboos University)

  • Lotfi Tadj

    (Saint Mary’s University
    Dalhousie University)

Abstract

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.

Suggested Citation

  • Lakhdar Aggoun & Lotfi Tadj, 2011. "Filtering and M-ary Detection in a Minimal Repair Maintenance Model," Springer Series in Reliability Engineering, in: Lotfi Tadj & M.-Salah Ouali & Soumaya Yacout & Daoud Ait-Kadi (ed.), Replacement Models with Minimal Repair, pages 207-221, Springer.
    • Handle: RePEc:spr:ssrchp:978-0-85729-215-5_8
    DOI: 10.1007/978-0-85729-215-5_8
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