Repairable consecutive-\(k\)-out-of-\(n:F\) system with Markov dependence. (English) Zbl 0953.90015
Summary: A model for a repairable consecutive-\(k\)-out-of-\(n:F\) system with Markov dependence is studied. A binary vector is used to represent the system state. The failure rate of a component in the system depends on the state of the preceding component. The failure risk of a system state is then introduced. On the basis of the failure risk, a priority repair rule is adopted. Then the transition density matrix can be determined, and the analysis of the system reliability can be conducted accordingly. One example each of a linear and a circular system is then studied in detail to explain the model and methodology developed in this paper.
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 90C40 | Markov and semi-Markov decision processes |
Keywords:
consecutive-\(k\)-out-of-\(n:F\) system; Markov dependence; binary system state; failure risk; \(Q\)-matrixReferences:
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