Computation and profit analysis of a $k$-out-of-$n$:$G$ repairable system under $N$-policy with multiple vacations and one replaceable repair facility

Wu, Wenqing; Tang, Yinghui; Yu, Miaomiao; Jiang, Ying

doi:10.1051/ro/2015001

Computation and profit analysis of a

k

-out-of-

n

G

repairable system under

N

-policy with multiple vacations and one replaceable repair facility

Wu, Wenqing ^1,² ; Tang, Yinghui ^1,² ; Yu, Miaomiao ³ ; Jiang, Ying ⁴

¹ Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610068, Sichuan, P.R. China.
² School of Mathematics & Software Science, Sichuan Normal University, 610068 Chengdu, Sichuan, P.R. China.
³ School of Science, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, P.R. China.
⁴ School of Science, Southwest University of Science and Technology, 621000 Mianyang, Sichuan, P.R. China.

RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 4, pp. 717-734.

Résumé

This paper considers a $k$ -out-of- $n$ : $G$ system with $N$ -policy and one repairman who takes multiple vacations, in which the operating times and repair times of components are governed by exponential distributions. Once an operating component breaks down, it is repaired by a repair facility. Moreover, the repair facility is subject to failure during the repair period which results in repair interruptions. Failed repair facility resumes repair after a random period of time. Under such assumptions, applying the quasi-birth-and-death process and the matrix-analytical approach, the system state probabilities are derived. In addition, various steady-state system performance measures such as the availability and the rate of occurrence of failure along with some numerical illustrations are reported. Finally, under a profit structure, we use the direct search method and the parabolic method to search for the optimal system parameters.

Reçu le : 2013-09-16
Accepté le : 2014-12-19

Zbl | 1 citation dans Numdam

DOI : 10.1051/ro/2015001

Classification : 60K20, 90B25
Mots-clés : k-out-of-n:Grepairable system, replaceable repair facility, matrix-analytical approach, performance measures, profit analysis

Affiliations des auteurs :

Wu, Wenqing ^{1, 2} ; Tang, Yinghui ^{1, 2} ; Yu, Miaomiao ³ ; Jiang, Ying ⁴

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     title = {Computation and profit analysis of a $k$-out-of-$n$:$G$ repairable system under $N$-policy with multiple vacations and one replaceable repair facility},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Wu, Wenqing; Tang, Yinghui; Yu, Miaomiao; Jiang, Ying. Computation and profit analysis of a $k$-out-of-$n$:$G$ repairable system under $N$-policy with multiple vacations and one replaceable repair facility. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 4, pp. 717-734. doi : 10.1051/ro/2015001. http://www.numdam.org/articles/10.1051/ro/2015001/

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