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The reliability analysis of k-out-of-n system based on Phase-type distribution
CHEN Tong, LI Fang, DI Peng
Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (1) : 260-266.
PDF(687 KB)
PDF(687 KB)
The reliability analysis of k-out-of-n system based on Phase-type distribution
This research investigates a k-out-of-n system in which the operational, standby and repair time of units follow continuous Phase-type distribution, instead of exponential distribution or other typical distributions. The proposed model provides an analytic reliability model that is more suitable to characterize the real situation. The stationary distribution is built by using matrix analytic methods; and several performance measures of interest, such as the system stationary availability, operational time, mean time between failures (MTBF) and failure arrival rate, are obtained. Finally, the validity and applicability of the model are implemented by numerical applications; and the influences of k on the system reliability laws are demonstrated when the value of n is fixed.
k-out-of-n system / reliability / Phase-type distribution {{custom_keyword}} /
[1] Myers A. Complex system reliability[M], London: Springer-Verlag, 2010.
[2] Xing L, Amar S, Wang C. Reliability of k-out-of-n systems with phased-mission requirements and imperfect fault coverage[J]. Reliability Engineering and System Safety, 2012, 103: 45-50.
[3] Moghaddass R, Zuo M J, Wang W B. Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth-death process[J]. Reliability Engineering and System Safety, 2011, 96(4): 489-496.
[4] Navarro J, Rubio R. Comparisons of coherent systems with non-identically distributed components[J]. Journal of Statistical Planning and Inference, 2012, 142(6): 1310-1319.
[5] Neuts M F, Meier K S. On the use of phase type distributions in reliability modelling of systems with two components[J]. OR Spektrum, 1981, 2(4): 227-234.
[6] Faddy M J. Phase-type distributions for failure times[J]. Mathematical and Computer Modelling, 1995, 22(10-12): 63-70.
[7] Gruruajan M, Srinivasan B. A complex two-unit system with random breakdown of repair facility[J]. Microelectronics Reliability, 1995, 35(2): 299-302.
[8] Montoro-Cazorla D, Pérez-Ocón R. A deteriorating two-system with two repair modes and sojourn times phase-type distributed[J]. Reliability Engineering and System Safety, 2006, 91(1): 1-9.
[9] Chakravarthy S R, Gómez-Corral A. The influence of delivery times on repairable k-out-of-N systems with spares[J]. Applied Mathematical Modelling, 2009, 33(5): 2368-2387.
[10] Barron Y, Frostig E, Levikson B. Analysis of R out of N systems with several repairmen, exponential life times and phase type repair times: An algorithmic approach[J]. European Journal of Operational Research, 2006, 169(1): 202-225.
[11] Ruiz-Castro J E, Li Q L. Algorithm for a general discrete k-out-of-n:G system subject to several types of failure with an indefinite number of repairpersons[J]. European Journal of Operational Research, 2011, 211(1): 97-111.
[12] Kenzin M, Frostig E. M out of n inspected systems subject to shocks in random environment[J]. Reliability Engineering and System Safety, 2009, 94(8): 1322-1330.
[13] Kao E P C. An introduction to stochastic processes[M]. Beijing: China Machine Press, 2006.
[14] 田乃硕. 休假随机服务系统[M]. 北京: 北京大学出版社, 2001. Tian Naishuo. Stochastic service system with vacation policies[M]. Beijing: Peking University Press, 2001.
[15] Breuer L, Baum D. An introduction to queueing theory and matrix-analytic methods[M]. Dordrecht: Springer, 2005.
[16] 冯懿, 左德承, 李金锋,等. 多态k-out-of-n:G型系统可用性评测[J]. 清华大学学报(自然科学版), 2011, 51(S1): 1515-1518. Feng Yi, Zuo Decheng, Li Jinfeng, et al. Availability evaluation of multi-state k-out-of-n:G systems[J]. Journal of Tsinghua University (Science & Technology), 2011, 51(S1): 1515-1518.
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