On the mean and extreme distances between failures in Markovian binary sequences

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2011

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Elsevier Science Bv

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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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Abstract

This paper is concerned with the mean, minimum and maximum distances between two successive failures in a binary sequence consisting of Markov dependent elements. These random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes. Exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented. (C) 2011 Elsevier B.V. All rights reserved.

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Yalcin, Femin/0000-0003-0602-9392; Eryilmaz, Serkan/0000-0002-2108-1781
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Yalcin, Femin ORCID logo
Eryilmaz, Serkan ORCID logo

Keywords

Binary sequence, Exact distribution, Extremes, Markov chain, System reliability

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5

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Volume

236

Issue

6

Start Page

1502

End Page

1510

URI

https://doi.org/10.1016/j.cam.2011.09.013
 https://hdl.handle.net/20.500.14411/1337

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