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Mathematical Problems in Engineering
Volume 2012, Article ID 106359, 8 pages
Research Article

Consecutive 𝑘 -within- 𝑚 -out-of- 𝑛 :F System with Nonidentical Components

Department of Industrial Engineering, Atilim University, Incek, 06836 Ankara, Turkey

Received 6 September 2011; Revised 7 December 2011; Accepted 8 December 2011

Academic Editor: Alexander P. Seyranian

Copyright © 2012 Serkan Eryilmaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As a generalisation of consecutive 𝑘 -out-of- 𝑛 :F and 𝑘 -out-of- 𝑛 :F system models, a consecutive 𝑘 -within- 𝑚 -out-of- 𝑛 :F system consists of 𝑛 linearly ordered components and fails if and only if there are 𝑚 consecutive components which include among them at least 𝑘 failed components. In this paper, we study the survival function of a consecutive 𝑘 -within- 𝑚 -out-of- 𝑛 :F system consisting of independent but nonidentical components. We obtain exact expressions for the survival function when 2 𝑚 𝑛 . A detailed analysis for consecutive 2-within- 𝑚 -out-of- 𝑛 :F systems is presented and the asymptotic behaviour of hazard rate of these systems is investigated using mixture representations.