Analysis of a Repairable k-out-of-n:G System with Expert Repairman's Multiple Vacations and Shut off Rule
Yuanyuan Zhang
School of Science, Southwest University of Science and Technology, Mianyang, China.
Wenqing Wu *
School of Science, Southwest University of Science and Technology, Mianyang, China.
Yinghui Tang
School of Mathematics and Software Science, Sichuan Normal University, Chengdu, China.
*Author to whom correspondence should be addressed.
Abstract
This paper investigates an k-out-of-n:G repairable system with expert repairman’s multiple vacations and continuous operation rule where the operating times and the repair times of components follow exponential distributions. When there is no failed component in the system, the expert repairman leaves for a vacation, the duration of which is governed by a phase type distribution. Once an operating component fails during his/her vacation period, it is repaired by an ordinary repairman. The ordinary repairman becomes inactivated when there is no failed component or the expert repairman returns from the vacation. Employing the matrix analytical method, we obtain the transient system availability, the rate of occurrence of failures at time t, the system reliability, the stationary availability, the stationary rate of occurrence of failures, and the mean time to failure of the system. Further, we discuss the time-dependent behaviour of the system reliability measures under different initial system states. Finally, special cases of the system are given to show the correctness of our results.
Keywords: k-out-of-n, G system, multiple vacations, continuous operation, matrix analytical method, reliability measures