On the Failure Rates of Consecutive−k−out−of−n Systems

Author:

Hwang F.K.,Yao Y.C.

Abstract

It is known that the lifetime of a k−out−of−n system has increasing failure rate (IFR) if all of its components have independent and identically distributed IFR lifetimes. Derman, Lieberman, and Ross raised the same question for consecutive−k−out−of−n systems. But the scarcity of results gives no clue as to whether most of such systems have IFR's. In this paper, we completely solve the k = 2 and k = 3 cases. We prove that these systems, with a handful of exceptions, do not have IFR's (contradicting the result of Derman, Lieberman, and Ross that a consecutive-2-out-of-n cycle has IFR for any n). Our result suggests the conjecture that for every fixed k there exists nk such that for every n ≧ nk a consecutive-k−out−of−n system does not have IFR. We also prove that for every fixed d there exists nd large enough such that for all n ≧ nd a consecuive.(n – d)−out−of−n system has IFR. In particular, if the system is a line, then nd = 3d +1 for d ≧ 1.

Publisher

Cambridge University Press (CUP)

Subject

Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability

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1. On the Closure of Aging Classes Under the Formation of Coherent Structures;International Journal of Reliability, Quality and Safety Engineering;2021-06-25

2. ON THE SIGNATURE OF COHERENT SYSTEMS AND APPLICATIONS;Probability in the Engineering and Informational Sciences;2007-12-18

3. The IFR property for consecutive-k-out-of-n:F systems;Statistics & Probability Letters;2002-10

4. The Increasing Failure Rate Property of Consecutive-k:-out-of-n Systems;Probability in the Engineering and Informational Sciences;1995-04

5. Consecutive-k-out-of-n Systems;Fundamental Studies in Engineering;1993

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