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

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. .
wwqing0704@163.com; tangyh@uestc.edu.cn
³ School of Science, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, P.R. China.
mmyu75@163.com
⁴ School of Science, Southwest University of Science and Technology, 621000 Mianyang, Sichuan, P.R. China.
xsjy2000@163.com

Received: 16 September 2013
Accepted: 19 December 2014

Abstract

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.