Interval uneffectiveness distribution for a k-out-of-n multistate reliability system with repair. (English) Zbl 0652.90050
The authors consider a system consisting of n identical parallel units, of which at most k units operate simultaneously. If more than k units are available, the superfluous units are put on cold standby and they cannot fail. If less than k units are available, the system operates at a proportionally reduced level. Moreover, all failed units can be under repair simultaneously (there are ample repair facilities). The lifetimes and repair times of the units are iid random variables belonging to the class of phase-type distributions with two phases. In the paper a method based on an approximation of this system by a two-state single component is given for the calculation of the probability distribution of that proportion of the system capacity that cannot be used in a given time period. The results are justified by Monte-Carlo simulations and their sensitivity to the distributional form of the lifetimes and repair times is investigated.
Reviewer: T.Cipra
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |
| 62N05 | Reliability and life testing |
Keywords:
effectiveness; Markov process; k-out-of-n system; identical parallel units; cold standby; lifetimes; repair times; phase-type distributions; approximation; two-state single component; Monte-Carlo simulationsReferences:
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