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Stochastic modelling of operational quality of k-out-of-n systems

Author

Listed:
  • Ji Hwan Cha

    (Ewha Womans University)

  • Maxim Finkelstein

    (University of the Free State
    ITMO University)

Abstract

In this paper, we study some operational quality measures of the k-out-of-n systems. Performance of these systems is characterized by a quality (output) function that is decreasing in the absence of components’ failures. Moreover, it decreases (downward jump) with each failure of a component in a system as well. We employ the point processes approach for description of the corresponding failure process and derivation of the main results. Expectations (unconditional and conditional on survival) and variability for the system’s quality function are derived and analyzed. The corresponding ‘future quality process’ is defined and described. Some illustrative examples are presented.

Suggested Citation

  • Ji Hwan Cha & Maxim Finkelstein, 2020. "Stochastic modelling of operational quality of k-out-of-n systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 424-441, July.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:2:d:10.1007_s11750-019-00536-y
    DOI: 10.1007/s11750-019-00536-y
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    References listed on IDEAS

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    1. Hsieh, Chung-Chi & Chiu, Kuo-Chang, 2002. "Optimal maintenance policy in a multistate deteriorating standby system," European Journal of Operational Research, Elsevier, vol. 141(3), pages 689-698, September.
    2. Namir Ghoraf, 2008. "Reliability formula & limit law of the failure time of “m-consecutive-k-out-of-n:F system”," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 62-72, July.
    3. N. Ghoraf & M. Boushaba, 2003. "Fast formula of a reliability ofm-consecutive-k-out-of-n:F system with cyclek," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 275-283, December.
    4. Marichal, Jean-Luc & Mathonet, Pierre & Navarro, Jorge & Paroissin, Christian, 2017. "Joint signature of two or more systems with applications to multistate systems made up of two-state components," European Journal of Operational Research, Elsevier, vol. 263(2), pages 559-570.
    5. Jorge Navarro & Maria Longobardi & Franco Pellerey, 2017. "Comparison results for inactivity times of k-out-of-n and general coherent systems with dependent components," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 822-846, December.
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Linear multistate consecutively-connected systems subject to a constrained number of gaps," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 246-252.
    7. Yeh, Wei-Chang, 2008. "A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 125-136.
    8. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, September.
    9. A. Krishnamoorthy & P. Ushakumari, 1999. "Reliability of ak-out-of-n system with repair and retrial of failed units," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 293-304, December.
    10. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    11. Ji Hwan Cha & Maxim Finkelstein, 2018. "Point Processes for Reliability Analysis," Springer Series in Reliability Engineering, Springer, number 978-3-319-73540-5, September.
    12. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
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