Reliability of Combined <i>m</I>-consecutive-<i>k< and Consecutive <i>k<sub>c</Sub>< Systems

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2012

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Ieee-inst Electrical Electronics Engineers inc

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Industrial Engineering
(1998)
Industrial Engineering is a field of engineering that develops and applies methods and techniques to design, implement, develop and improve systems comprising of humans, materials, machines, energy and funding. Our department was founded in 1998, and since then, has graduated hundreds of individuals who may compete nationally and internationally into professional life. Accredited by MÜDEK in 2014, our student-centered education continues. In addition to acquiring the knowledge necessary for every Industrial engineer, our students are able to gain professional experience in their desired fields of expertise with a wide array of elective courses, such as E-commerce and ERP, Reliability, Tabulation, or Industrial Engineering Applications in the Energy Sector. With dissertation projects fictionalized on solving real problems at real companies, our students gain experience in the sector, and a wide network of contacts. Our education is supported with ERASMUS programs. With the scientific studies of our competent academic staff published in internationally-renowned magazines, our department ranks with the bests among other universities. IESC, one of the most active student networks at our university, continues to organize extensive, and productive events every year.

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A combined m-consecutive-k-out-of-n:F & consecutive-k(c)-out-of-n:F system consists of linearly ordered components, and fails iff there exist at least k(c) consecutive failed components, or at least m non-overlapping runs of k consecutive failed components. This structure has applications for modeling systems such as infrared detecting and signal processing, and bank automatic payment systems. In this paper, we derive a combinatorial equation for the number of path sets of this structure including a specified number of working components. This number is used to derive a reliability function, and a signature based survival function formulae, for the system consisting of i.i.d. components. We also obtain a combinatorial equation for the reliability of a system with Markov dependent components.

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Eryilmaz, Serkan/0000-0002-2108-1781
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Keywords

Consecutive k(c)-out-of-n:F system, m-consecutive-k-out-of-n:F system, Markov dependence, mean time to failure, runs, signature, survival function

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Volume

61

Issue

1

Start Page

215

End Page

219

URI

https://doi.org/10.1109/TR.2011.2182401
 https://hdl.handle.net/20.500.14411/1361

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