The number of failed components upon system failure when the lifetimes are discretely distributed

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2022

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Elsevier Sci Ltd

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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

The number of failed components at the time when the system fails is an important quantity which can be effectively used in the determination of the optimal number of spares. This paper is concerned with the distribution and expected value of this quantity when the lifetimes of a given coherent system are discretely distributed. In particular, the distribution of the corresponding random quantity is derived for all coherent systems of order three and four. The mean number of the failed components upon system failure is exactly derived for a linear consecutive-2-out-of-n:F structure. The mean of the quantity under concern is also computed for series and parallel systems consisting of disjoint modules. The latter computation provides an efficient way to obtain the corresponding mean for a larger system via the modules which have smaller number of components.

Description

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

Keywords

Coherent system, Discrete distributions, Modules, Consecutive-k-out-of-n, F system

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6

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225

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https://doi.org/10.1016/j.ress.2022.108632
 https://hdl.handle.net/20.500.14411/1799

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