Reliability Model of Multi-state Repairable Systems with Different Repair Effects

doi:10.3969/j.issn.1000-1093.2014.09.023

Abstract

Abstract: Three repair effects, namely repairing some system and making it as same as the original, imperfect and perfect, are proposed to research the reliability model of multi-state repairable systems with the different repair effects. The operating state is divided into two classes: good and general; the operation and repair times of system are assumed to submit to continuous phase-type distribution. An infinitesimal generator matrix for the Markov transfer among system states is established, and the stationary probability vector is achieved. The proposed model provides the analytic expressions of the stationary availability and failure rate. Finally, the numerical examples are given to illustrate the effectiveness and applicability of model.

Key words: ordnance science and technology, multi-state, reliability, repair effect, phase-type distribution

CLC Number:

F253.4

DI Peng, LI Fang, CHEN Tong. Reliability Model of Multi-state Repairable Systems with Different Repair Effects[J]. Acta Armamentarii, 2014, 35(9): 1488-1494.

References

［1］ Zio E. Reliability engineering:old problems and new challenges[J]. Reliability Engineering and System Safety, 2009,94: 125-141.
[2] Ying K G,Jing L. Multi-state system reliability: a new and systematic review[J]. Procedia Engineering, 2011, 29: 531-536.
[3] Barlow R E, Wu A S. Coherent systems with multi-state components[J], Mathematics of Operations Research, 1978, 3: 275-281.
[4] Lisnianski A, Frenkel I, Ding Y. Multi-state system reliability analysis and optimization for engineers and industrial managers[M], London: Springer, 2010:8-19.
[5] Amico G D, Biase G D,Manca R. A customer’s utility measure based on the reliabilityof multi-state systems[J]. Decisions in Economics Finance, 2011,34(1):1-20.
[6] Lisnianski A, Elmakias D, Laredo D, et al. A multi-state Markov model for a short-term reliability analysis of a power generatingunit[J]. Reliability Engineering and System Safety, 2012, 98(1): 1-6.
[7] Levitin G, Xing L. Reliability and performance of multi-state systems with propagated failure shaving selective effect[J]. Reliability Engineering and System Safety, 2010, 95: 655-661.
[8] Moghaddass R, Zuo M. A parameter estimation method for a condition-monitored device under multi-state deterioration[J]. Reliability Engineering and System Safety, 2012, 106: 94-103.
[9] 王丽花, 岳德权, 张静, 等. 具有小修和一般型更换策略的多状态退化系统[J]. 辽宁工程技术大学学报:自然科学版, 2011,30(6):935-938.
WANG Li-hua, YUE De-quan, ZHANG Jing, et al. A multi-state degraded system with minimal repairs and the replacement policy in general distribution[J]. Journal of Liaoning Technical University:Natural Science, 2011, 30(6):935-938.(in Chinese)
[10] Yuan L, Xu J. A deteriorating system with its repairman having multiple vacations[J]. Applied Mathematics and Computation, 2011,217(10):4980-4989.
[11] Frostig E, Kenzin M. Availability of inspected systems subject to shocks-a matrix algorithmic approach[J]. European Journal of Operational Research, 2009,193(1): 168-183.
[12] 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.
[13] Segovia M C, Labeau P E. Reliability of a multi-state system subject to shocks using phase-type distributions[J]. Applied Mathematical Modelling, 2013, 37(7):4883-4904.
[14] 陈童. 基于PH分布和马尔可夫到达过程的装备备件需求与库存模型研究[D]. 长沙: 国防科学技术大学, 2010.
CHEN Tong.Research on demand and inventory models of equipment spare parts based on phase-type distribution and Markovian arrival process[D]. Changsha: National University of Defense Technology, 2010.( in Chinese)
[15] 田乃硕. 休假随机服务系统[M].北京:北京大学出版社, 2001:5-7.
TIAN Nai-shuo. Queuing systems with sever vacations[M], Beijing:Peking University Press, 2001:5-7.( in Chinese)
[16] 黄卓.Phase-type分布数据拟合方法及其应用研究[D]. 长沙: 国防科学技术大学, 2007.
HUANG Zhuo.Research on phase-type distributions data fitting method and its applications[D]. Changsha:National University of Defense Technology, 2007.( in Chinese)

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