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A Stochastic Hybrid Systems framework for analysis of Markov reward models

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  • Dhople, S.V.
  • DeVille, L.
  • Domínguez-García, A.D.

Abstract

In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: (i) a discrete state that describes the possible configurations/modes that a system can adopt, which includes the nominal (non-faulty) operational mode, but also those operational modes that arise due to component faults, and (ii) a continuous state that describes the reward. Discrete state transitions are stochastic, and governed by transition rates that are (in general) a function of time and the value of the continuous state. The evolution of the continuous state is described by a stochastic differential equation and reward measures are defined as functions of the continuous state. Additionally, each transition is associated with a reset map that defines the mapping between the pre- and post-transition values of the discrete and continuous states; these mappings enable the definition of impulses and losses in the reward. The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models. We illustrate the application of the framework to performability analysis via analytical and numerical examples.

Suggested Citation

  • Dhople, S.V. & DeVille, L. & Domínguez-García, A.D., 2014. "A Stochastic Hybrid Systems framework for analysis of Markov reward models," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 158-170.
    • Handle: RePEc:eee:reensy:v:123:y:2014:i:c:p:158-170
    DOI: 10.1016/j.ress.2013.10.011
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    References listed on IDEAS

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    1. Bucci, Paolo & Kirschenbaum, Jason & Mangan, L. Anthony & Aldemir, Tunc & Smith, Curtis & Wood, Ted, 2008. "Construction of event-tree/fault-tree models from a Markov approach to dynamic system reliability," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1616-1627.
    2. Lisnianski, Anatoly & Elmakias, David & Laredo, David & Ben Haim, Hanoch, 2012. "A multi-state Markov model for a short-term reliability analysis of a power generating unit," Reliability Engineering and System Safety, Elsevier, vol. 98(1), pages 1-6.
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    4. Koutras, Vasilis P. & Platis, Agapios N. & Gravvanis, George A., 2007. "On the optimization of free resources using non-homogeneous Markov chain software rejuvenation model," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1724-1732.
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    6. Domínguez-García, Alejandro D. & Kassakian, John G. & Schindall, Joel E. & Zinchuk, Jeffrey J., 2008. "An integrated methodology for the dynamic performance and reliability evaluation of fault-tolerant systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1628-1649.
    7. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2013. "A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 294-299.
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    Cited by:

    1. Anil Kr. Aggarwal & Sanjeev Kumar & Vikram Singh, 2017. "Performance modeling of the serial processes in refining system of a sugar plant using RAMD analysis," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1910-1922, November.
    2. Anil Kr. Aggarwal & Sanjeev Kumar & Vikram Singh, 2017. "Mathematical modeling and reliability analysis of the serial processes in feeding system of a sugar plant," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(1), pages 435-450, January.
    3. Raoni, Rafael & Secchi, Argimiro R., 2019. "Procedures to model and solve probabilistic dynamic system problems," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    4. Fan, Mengfei & Zeng, Zhiguo & Zio, Enrico & Kang, Rui & Chen, Ying, 2018. "A stochastic hybrid systems model of common-cause failures of degrading components," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 159-170.
    5. Anil Kr. Aggarwal & Vikram Singh & Sanjeev Kumar, 2017. "Availability analysis and performance optimization of a butter oil production system: a case study," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(1), pages 538-554, January.

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