A Markov repairable system with history-dependent up and down states is presented. The state
space of the repairable system is divided into three sets, which are up states, down states and changeable states.
Using aggregated stochastic processes, we can get the multi-interval availability and multi-point availability for
the Markov repairable system. Finally, numerical examples are given to illustrate the obtained results.
WANG Wen-guang (王文光), DU Shi-jia* (杜时佳), CUI Li-rong (崔利荣)
. Multi-Point and Multi-Interval Availabilities for Markov Repairable Systems with History-Dependent Up and Down States[J]. Journal of Shanghai Jiaotong University(Science), 2015
, 20(3)
: 349
-352
.
DOI: 10.1007/s12204-015-1635-6
[1] Guo H R, Liao H T, ZhaoWB, et al. A new stochastic model for systems under general repairs [J]. IEEE Transactions on Reliability, 2007, 56(1), 40-49.
[2] Moghaddass R, Zuo M J, Qu J. Reliability and availability analysis of a repairable k-out-of-n: G system with r repairmen subject to shut-off rules [J].IEEE Transactions on Reliability, 2011, 60(3), 658-666.
[3] Wang Y, Pham H. A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk systems with hidden failure [J]. IEEE Transactions on Reliability, 2011, 60(4), 770-781.
[4] Cui L R, Du S J, Hawkes A G. A study on a singleunit repairable system with state aggregations [J]. IIE Transactions, 2012, 44, 1022-1032.
[5] Guo H T, Yang X H. Automatic creation of Markov models for reliability assessment of safety instrumented systems [J]. Reliability Engineering and System Safety,2008, 93(6), 829-837.
[6] Colquhoun D, Hawkes A G. On the stochastic properties of bursts of single ion channel openings and of clusters of bursts [J]. Philosophical Transactions of Royal Society, London. Series B: Biological Sciences,1982, 300, 1-59.
[7] Zheng Z H, Cui L R, Hawkes A G. A study on a single-unit Markov repairable system with repair time omission [J]. IEEE Transactions on Reliability, 2006,55(2), 182-188.
[8] Cui L R, Li H J, Li J L. Markov repairable systems with history-dependent up and down states [J].Stochastic Models, 2007, 23, 665-681.
[9] Cui L R, Du S J, Zhang A F. Reliability measures for two-part partition of states for aggregated Markov repairable systems [J]. Annals of Operations Research,2014, 212(1), 93-114.
[10] Sericola B. Interval-Availability distribution of 2-state systems with exponential failures and phase-type repairs [J]. IEEE Transactions on Reliability, 1994, 43(2), 335-343.
[11] Cui L R, Du S J, Liu B L. Multi-point and multiinterval availabilities [J]. IEEE Transactions on Reliability,2013, 62(4), 811-820.
