Reliability analysis of a k-out-of-n:G repairable system with single vacation

Abstract This paper analyzes a k-out-of-n:G repairable system with one repairman who takes a single vacation, the duration of which follows a general distribution. The working time of each component is an exponentially distributed random variable and the repair time of each failed component is governed by an arbitrary distribution. Moreover, we assume that every component is “as good as new” after being repaired. Under these assumptions, several important reliability measures such as the availability, the rate of occurrence of failures, and the mean time to first failure of the system are derived by employing the supplementary variable technique and the Laplace transform. Meanwhile, their recursive expressions are obtained. Furthermore, through numerical examples, we study the influence of various parameters on the system reliability measures. Finally, the Monte Carlo simulation and two special cases of the system which are ( n - 1 ) -out-of-n:G repairable system and 1-out-of-n:G repairable system are presented to illustrate the correctness of the analytical results.

[1]  Quan-Lin Li,et al.  Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons , 2011, Eur. J. Oper. Res..

[2]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[3]  Jau-Chuan Ke,et al.  Batch arrival queue with N-policy and at most J vacations , 2010 .

[4]  Achyutha Krishnamoorthy,et al.  k-out-of-n-system with repair:T-policy , 2001 .

[5]  Antonio Gómez-Corral,et al.  The influence of delivery times on repairable k-out-of-N systems with spares , 2009 .

[6]  Yinghui Tang,et al.  A deteriorating repairable system with stochastic lead time and replaceable repair facility , 2012, Comput. Ind. Eng..

[7]  Wen Lea Pearn,et al.  The randomized vacation policy for a batch arrival queue , 2010 .

[8]  Hyun Gook Kang,et al.  Unavailability and spurious operation probability of k-out-of-n reactor protection systems in consideration of CCF , 2012 .

[9]  A. Krishnamoorthy,et al.  k-out-of-n-system with repair: The N-policy , 2002 .

[10]  Bin Liu,et al.  Transient analysis of an M , 2008, Eur. J. Oper. Res..

[11]  Jiandong Li,et al.  RELIABILITY ANALYSIS OF AN N-COMPONENT SERIES SYSTEM WITH M FAILURE MODES AND VACATION , 2008 .

[12]  A. Krishnamoorthy,et al.  k-out-of-n system with repair: the max(N, T) policy , 2004, Perform. Evaluation.

[13]  A. Krishnamoorthy,et al.  k-out-of-n: G system with repair: the D-policy , 2001, Comput. Oper. Res..

[14]  Abdelhakim Khatab,et al.  Availability of K-out-of-N: G systems with non-identical components subject to repair priorities , 2009, Reliab. Eng. Syst. Saf..

[15]  Ming Jian Zuo,et al.  Availability of a general k-out-of-n: G system with non-identical components considering shut-off rules using quasi-birth-death process , 2011, Reliab. Eng. Syst. Saf..

[16]  Michael Pecht,et al.  Reliability of a k-out-of-n warm-standby system , 1992 .

[17]  Jau-Chuan Ke,et al.  Batch arrival queues under vacation policies with server breakdowns and startup/closedown times , 2007 .

[18]  Quanlin Li,et al.  Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs , 2001, Queueing Syst. Theory Appl..

[19]  G. Arulmozhi,et al.  Exact equation and an algorithm for reliability evaluation of K-out-of-N: G system , 2002, Reliab. Eng. Syst. Saf..

[20]  Wang Jin-ting.  Reliability analysis of M/G/1 queues with general retrial times and server breakdowns , 2006 .

[21]  Li Yuan.  Reliability analysis for a k-out-of-n: G system with redundant dependency and repairmen having multiple vacations , 2012, Appl. Math. Comput..

[22]  Shaomin Wu,et al.  Reliability analysis for a k/n(F) system with repairable repair-equipment , 2009 .

[23]  Xiaohu Li,et al.  Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down , 2006, Reliab. Eng. Syst. Saf..

[24]  Jaydev Sharma,et al.  State Transition Matrix and Transition Diagram of k-out-of-n-:G System With Spares , 1981, IEEE Transactions on Reliability.

[25]  Yinghui Tang,et al.  A phase-type geometric process repair model with spare device procurement and repairman's multiple vacations , 2013, Eur. J. Oper. Res..

[26]  Krishna B. Misra,et al.  Handbook of Performability Engineering , 2008 .