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Consecutive k out of n: F systems with Cycle k

✍ Scribed by Philip J. Boland; Stavros Papastavridis

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
85 KB
Volume
44
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 (16i6k)) 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.

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## Abstract As a generalization of __k__‐out‐of‐__n__:F and consecutive __k__‐out‐of‐__n__:F systems, the consecutive __k__‐within‐__m__‐out‐of‐__n__:F system consists of __n__ linearly ordered components such that the system fails iff there are __m__ consecutive components which include among them