A computational method for finding the availability of opportunistically maintained multi-state systems with non-exponential distributions

Naichao Wang, Yu Jin, Lin Ma, Haitao Liao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Availability is one of the most important performance measures of a repairable system. Among various mathematical methods, the method of supplementary variables is an effective way of modeling the steady-state availability of systems governed by non-exponential distributions. However, when all the underlying probability distributions are non-exponential (e.g., Weibull), the corresponding state equations are difficult to solve. To overcome this challenge, a new method is proposed in this article to determine the steady-state availability of a multi-state repairable system, where all the state sojourn times, as well as the maintenance times, are generally distributed. As an indispensable step, the well-posedness and stability of the system’s state equations are illustrated and proved using C0 operator semigroup theory. Afterwards, based on the generalized Integral Mean Value Theorem, the expression for system steady-state availability is derived as a function of state probabilities. Then, the original problem is transformed into a system of linear equations that can be easily solved. A simulation study and an instance studied in the literature are used to demonstrate the applications of the proposed method in practice. These numerical examples illustrate that the proposed method provides a new computational tool for effectively evaluating the availability of a repairable system without relying on simulation.

Original languageEnglish (US)
Pages (from-to)1047-1061
Number of pages15
JournalIISE Transactions
Volume52
Issue number9
DOIs
StatePublished - Sep 1 2020
Externally publishedYes

Keywords

  • Availability
  • corrective maintenance
  • multi-state system
  • non-exponential distributions
  • preventive maintenance

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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