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Consecutive k out of n: F systems with Cycle k

Author

Listed:
  • Boland, Philip J.
  • Papastavridis, Stavros

Abstract

An r consecutive k out of n: F system is a system of n linearly arranged components which fails if r non-overlapping sequences of k components fail. When r=1 we have the classic consecutive k out of n: F system about which there is an extensive literature. In this research we study the situation where there are k distinct components with failure probabilities qi for i=1,...,k and where the failure probability of the jth component (j=mk+i (1[less-than-or-equals, slant]i[less-than-or-equals, slant]k)) is qi. We call such a system an r consecutive k out of n: F system with cycle (or period) k. We obtain exact expressions for the failure probability of an r consecutive k out of n: F system and in particular show that it is independent of the order of the k components if n is a multiple of k. Interesting applications are given for the arrangement of sport competitions and inspection procedures in quality control.

Suggested Citation

  • Boland, Philip J. & Papastavridis, Stavros, 1999. "Consecutive k out of n: F systems with Cycle k," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 155-160, August.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:2:p:155-160
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    Cited by:

    1. Namir Ghoraf, 2008. "Reliability formula & limit law of the failure time of “m-consecutive-k-out-of-n:F system”," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 62-72, July.

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