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Technical Note

Calculating the Rate of Occurrence of Failures for Continuous-time Markov Chains with Application to a Two-component Parallel System

Pages 528-536 | Received 01 Oct 1992, Accepted 01 Jul 1994, Published online: 20 Dec 2017

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Guglielmo D?Amico. (2015) Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings. Methodology and Computing in Applied Probability 17:4, pages 929-949.
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Hongjun Sun & Lixia Ma. (2014) Modeling of a deteriorating system with single vacation and reliability analysis. Modeling of a deteriorating system with single vacation and reliability analysis.
Miaomiao Yu, Yinghui Tang, Yonghong Fu, Lemeng Pan & Xiaowo Tang. (2012) A deteriorating repairable system with stochastic lead time and replaceable repair facility. Computers & Industrial Engineering 62:2, pages 609-615.
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Ragi Krishnan & S. Somasundaram. (2011) Reliability analysis of repairable consecutive‐k‐out‐of‐n: G systems with sensor and repairmen. International Journal of Quality & Reliability Management 28:8, pages 894-908.
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James J. Cochran, Louis A. CoxJr.Jr., Pinar Keskinocak, Jeffrey P. Kharoufeh & J. Cole SmithMinjae Park & Hoang Pham. 2011. Wiley Encyclopedia of Operations Research and Management Science. Wiley Encyclopedia of Operations Research and Management Science.
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Qihong Duan, Zhiping Chen & Dengfu Zhao. (2010) An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains. Mathematical Problems in Engineering 2010, pages 1-16.
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E. Zio. (2009) Reliability engineering: Old problems and new challenges. Reliability Engineering & System Safety 94:2, pages 125-141.
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Wen-Long Wang & Gen-Qi Xu. (2009) Stability analysis of a complex standby system with constant waiting and different repairman criteria incorporating environmental failure. Applied Mathematical Modelling 33:2, pages 724-743.
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Yuan Lin Zhang. (2008) A geometrical process repair model for a repairable system with delayed repair. Computers & Mathematics with Applications 55:8, pages 1629-1643.
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Kit-Nam Leung. 2006. Springer Handbook of Engineering Statistics. Springer Handbook of Engineering Statistics 931 955 .
Y. Wu & J. Guan. (2005) Repairable Consecutive-k-Out-of-n: G Systems With<tex>$r$</tex>Repairmen. IEEE Transactions on Reliability 54:2, pages 328-337.
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Lam Yeh. (2016) A Monotone Process Maintenance Model for a Multistate System. Journal of Applied Probability 42:1, pages 1-14.
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Lam Yeh. (2016) A Monotone Process Maintenance Model for a Multistate System. Journal of Applied Probability 42:01, pages 1-14.
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R. Pérez-Ocón & J.E. Ruiz Castro. (2004) Two models for a repairable two-system with phase-type sojourn time distributions. Reliability Engineering & System Safety 84:3, pages 253-260.
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A.S. Ackleh, K. Deng, J. Derouen & Wei Li. (2004) A numerical method for a nonlocal hyperbolic model arising from a reliability system. Computers & Mathematics with Applications 47:1, pages 135-147.
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Yeh Lam & Yuan Lin Zhang. (2003) A geometric-process maintenance model for a deteriorating system under a random environment. IEEE Transactions on Reliability 52:1, pages 83-89.
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Richard C.M. Yam, Ming J. Zuo & Yuan Lin Zhang. (2003) A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n:F systems. Reliability Engineering & System Safety 79:1, pages 1-9.
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Yeh Lam & Hon Keung Tony Ng. (2001) A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k−1)-step Markov dependence. European Journal of Operational Research 129:3, pages 663-682.
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Marcel F. Neuts, Rafael Pérez-Ocón & Inmaculada Torres-Castro. (2016) Repairable models with operating and repair times governed by phase type distributions. Advances in Applied Probability 32:2, pages 468-479.
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Yuan Lin Zhang, Ming J. Zuo & Richard C.M. Yam. (2000) Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair. Reliability Engineering & System Safety 68:2, pages 113-120.
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Wei Li, Attahiru Sule Alfa & Yiqiang Q. Zhao. (1998) Stochastic analysis of a repairable system with three units and two repair facilities. Microelectronics Reliability 38:4, pages 585-595.
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Lam Yeh. (2016) The rate of occurrence of failures. Journal of Applied Probability 34:1, pages 234-247.
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Lam Yeh. (2016) The rate of occurrence of failures. Journal of Applied Probability 34:01, pages 234-247.
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