Reliability analysis of circular markov repairable systems with spatial dependence

Liying Wang, Shubin Si

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Aim. The introduction of the full paper reviews a number of papers on reliability models with dependent units in the open literature and proposes what we believe to be a new model mentioned in the title. The core of Section 1 consists of: (1) we present the assumptions of the circular Markov repairable systems with spatial dependence; (2) we put forward the Markov processes associated with the 4-unit and 5-unit circular Markov repairable systems with spatial dependence and define their states as indicated in Fig.1 and Fig. 2. Section 2 analyzes the state transitions of the 4-unit and 5-unit systems and obtains the state transition rate matrices corresponding to them. Section 3 discusses the instantaneous and asymptotic availabilities of the 4-unit and 5-unit systems, which are given by equations (3)-(5). Section 4 presents the numerical examples of the 4-unit and 5-unit systems. The curves of instantaneous availabilities are shown in Fig. 5 and Fig. 6. We obtain the conclusions that: (1) the system with independent units is more reliable than the circular Markov repairable system with spatial dependence; (2) the 5-unit circular Markov repairable system is more reliable than the 4-unit system.

Original languageEnglish
Pages (from-to)923-928
Number of pages6
JournalXibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University
Volume32
Issue number6
StatePublished - 1 Dec 2014

Keywords

  • Availability
  • Circular system
  • Differential equations
  • Inverse problems
  • Laplace transforms
  • Markov processes
  • Markov repairable system
  • Mathematical models
  • MATLAB
  • Matrix algebra
  • Probability
  • Reliability analysis
  • Spatial dependence.

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