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Optimal allocation of minimal repairs in parallel and series systems
Author(s) -
Zhang Yiying,
Zhao Peng
Publication year - 2019
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21865
Subject(s) - series (stratigraphy) , poisson distribution , reliability (semiconductor) , computer science , optimal allocation , mathematical optimization , hazard , component (thermodynamics) , failure rate , stochastic ordering , unit (ring theory) , work (physics) , mathematics , statistics , engineering , mechanical engineering , paleontology , power (physics) , physics , chemistry , mathematics education , organic chemistry , quantum mechanics , biology , thermodynamics
Abstract In reliability engineering, the concept of minimal repair describes that the repair brings the failed unit (eg, system or component) to the situation which is same as it was just before the failure. With the help of the well‐known Gamma‐Poisson relationship, this paper investigates optimal allocation strategies of minimal repairs for parallel and series systems through implementing stochastic comparisons of various allocation policies in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orderings. Numerical examples are presented to illustrate these findings as well. These results not only strengthen and generalize some known ones in the seminal work of Shaked and Shanthikumar, but also solve the open problems proposed by Chahkandi et al.'s study and Arriaza et al.'s study.