Analysis of a repairable k-out-of-n:G system with repairman's multiple delayed vacations

References

• J.H. Cao and K. Cheng, Introduction to Reliability Mathematical, Higher Education Press, Beijing, 2006.
   Google Scholar
• S.R. Chakravarthy and A. Gómez-Corral, The influence of delivery times on repairable k-out-of-N systems with spares, Appl. Math. Model. 33(5) (2009), pp. 2368–2387. doi: 10.1016/j.apm.2008.07.007
   Web of Science ®Google Scholar
• S.R. Chakravarthy, A. Krishnamoorthy, and P.V. Ushakumari, A k-out-of-n reliability system with an unreliable server and phase type repairs and services: The (N,T) policy, J. Appl. Math. Stoch. Anal. 14(4) (2001), pp. 361–380. doi: 10.1155/S1048953301000326
   Google Scholar
• L.P. Cheng, Z.-S. Ye, and M. Xie, Joint maintenance and spare component provisioning policy for k-out-of-n systems, Asia-Pac. J. Oper. Res. 30(6) (2013), pp. 1–21.
   Web of Science ®Google Scholar
• E. Frostig and B. Levikson, On the availability of R out of N repairable systems, Naval Res. Logist. 49(5) (2002), pp. 483–498. doi: 10.1002/nav.10025
   Web of Science ®Google Scholar
• S. Gao and Y.F. Yao, An MX/G/1 queue with randomized working vacations and at most J vacations, Int. J. Comput. Math. 91(3) (2014), pp. 368–383. doi: 10.1080/00207160.2013.790964
   Web of Science ®Google Scholar
• M.N. Gopalan and U.D. Kumar, On the transient behaviour of an r-our-of-n:G system, Microelectron. Reliab. 36(3) (1996), pp. 409–413. doi: 10.1016/0026-2714(95)00089-5
   Web of Science ®Google Scholar
• J.-C. Ke, K.-B. Huang, and W.L. Pearn, A batch arrival queue under randomised multi-vacation policy with unreliable server and repair, Int. J. Syst. Sci. 43(3) (2012), pp. 552–565. doi: 10.1080/00207721.2010.517863
   Web of Science ®Google Scholar
• A. Khatab, N. Nahas, and M. Nourelfath, Availability of k-out-of-n:G systems with non-identical components subject to repair priorities, Reliab. Eng. Syst. Saf. 94(2) (2009), pp. 142–151. doi: 10.1016/j.ress.2008.02.017
   Web of Science ®Google Scholar
• A. Krishnamoorthy, V.C. Narayanan, and T.G. Deepak, Reliability of a k-out-of-n system with repair by a service station attending a queue with postponed work, Int. J. Reliab. Qual. Safety Eng. 14(4) (2007), pp. 379–398. doi: 10.1142/S0218539307002702
   Google Scholar
• W. Kuo and M.J. Zuo, Optimal Reliability Modeling: Principles and Applications, John Wiley & Sons, New York, 2003.
   Google Scholar
• H. Li and Y.X. Zhu, Analysis of M/G/1 queues with delayed vacations and exhaustive service discipline, European J. Oper. Res. 92(1) (1996), pp. 125–134. doi: 10.1016/0377-2217(94)00364-5
   Web of Science ®Google Scholar
• X.H. Li, M.J. Zuo, and R.C. Yam, Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down, Reliab. Eng. Syst. Saf. 91(3) (2006), pp. 305–310. doi: 10.1016/j.ress.2005.01.010
   Web of Science ®Google Scholar
• R. Moghaddass, M.J. Zuo, and W.B. Wang, Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth-death process, Reliab. Eng. Syst. Saf. 96(4) (2011), pp. 489–496. doi: 10.1016/j.ress.2010.12.001
   Web of Science ®Google Scholar
• J.E. Ruiz-Castro and Q.L. Li, Algorithm for a discrete k-out-of-n:G system subject to several types of failure with an indefinite number of repairpersons, European J. Oper. Res. 211(1) (2011), pp. 91–111. doi: 10.1016/j.ejor.2010.10.024
   Web of Science ®Google Scholar
• D.-H. Shi, Probability analysis of the repairable queueing system M/G(Ek/H)/1, Ann. Oper. Res. 24(1) (1990), pp. 185–203. doi: 10.1007/BF02216823
   Google Scholar
• K.S. de Smidt-Destombes, M.C. van der Heijden, and A. van Harten, On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy, Reliab. Eng. Syst. Saf. 83(3) (2004), pp. 287–300. doi: 10.1016/j.ress.2003.10.004
   Web of Science ®Google Scholar
• K.S. de Smidt-Destombes, M.C. van der Heijden, and A. van Harten, Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity, Int. J. Prod. Econ. 107(2) (2007), pp. 404–421. doi: 10.1016/j.ijpe.2006.08.013
   Web of Science ®Google Scholar
• Y.H. Tang, X. Yun, and S.J. Huang, Reliability indices of discrete–time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations, J. Syst. Sci. Complexity 25(6) (2012), pp. 1122–1135. doi: 10.1007/s11424-012-1062-9
   Google Scholar
• N.S. Tian and Z.G. Zhang, Vacation Queueing Models – Theory and Applications, Springer–Verlag, New York, 2006.
   Google Scholar
• P.V. Ushakumari and A. Krishnamoorthy, k-out-of-n system with repair: The max (N,T) policy, Perform. Eval. 57(2) (2004), pp. 221–234. doi: 10.1016/j.peva.2003.10.006
   Web of Science ®Google Scholar
• M.M. Yu, Y.H. Tang, Y.H. Fu, and L.M. Pan, GI/Geom/1/N/MWV queue with changeover time and searching for the optimum service rate in working vacation period, J. Comput. Appl. Math. 235(2) (2011), pp. 2170–2184. doi: 10.1016/j.cam.2010.10.013
   Web of Science ®Google Scholar
• L. Yuan, Reliability analysis for a k-out-of-n:G system with redundant dependency and repairmen having multiple vacations, Appl. Math.d Comput. 218(24) (2012), pp. 11959–11969. doi: 10.1016/j.amc.2012.06.006
   Web of Science ®Google Scholar
• Y.L. Zhang and S.M. Wu, Reliability analysis for a k/n(F) system with repairable repair-equipment, Appl. Math. Model. 33(7) (2009), pp. 3052–3067. doi: 10.1016/j.apm.2008.10.022
   Web of Science ®Google Scholar