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Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems

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  • Bent Natvig

    (University of Oslo)

Abstract

In Natvig and Gåsemyr (Methodol Comput Appl Probab 11:603–620, 2009) dynamic and stationary measures of importance of a component in a binary system were considered. To arrive at explicit results the performance processes of the components were assumed to be independent and the system to be coherent. Especially the Barlow–Proschan and the Natvig measures were treated in detail and a series of new results and approaches were given. For the case of components not undergoing repair it was shown that both measures are sensible. Reasonable measures of component importance for repairable systems represent a challenge. A basic idea here is also to take a so-called dual term into account. For a binary coherent system, according to the extended Barlow–Proschan measure a component is important if there are high probabilities both that its failure is the cause of system failure and that its repair is the cause of system repair. Even with this extension results for the stationary Barlow–Proschan measure are not satisfactory. For a binary coherent system, according to the extended Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. With this extension the results for the stationary Natvig measure seem very sensible. In the present paper most of these results are generalized to multistate strongly coherent systems. For such systems little has been published until now on measures of component importance even in the nonrepairable case.

Suggested Citation

  • Bent Natvig, 2011. "Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 523-547, September.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:3:d:10.1007_s11009-010-9170-2
    DOI: 10.1007/s11009-010-9170-2
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    References listed on IDEAS

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    1. Barlow, Richard E. & Proschan, Frank, 1975. "Importance of system components and fault tree events," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 153-173, April.
    2. Natvig, Bent & Eide, Kristina A. & Gåsemyr, Jørund & Huseby, Arne B. & Isaksen, Stefan L., 2009. "Simulation based analysis and an application to an offshore oil and gas production system of the Natvig measures of component importance in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1629-1638.
    3. Bent Natvig & Jørund Gåsemyr, 2009. "New Results on the Barlow–Proschan and Natvig Measures of Component Importance in Nonrepairable and Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 603-620, December.
    4. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
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    Cited by:

    1. Shumin Li & Shubin Si & Liudong Xing & Shudong Sun, 2014. "Integrated importance of multi-state fault tree based on multi-state multi-valued decision diagram," Journal of Risk and Reliability, , vol. 228(2), pages 200-208, April.
    2. Serkan Eryilmaz, 2013. "Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 313-320, June.
    3. Rocco S., Claudio M. & Ramirez-Marquez, Jose Emmanuel, 2012. "Innovative approaches for addressing old challenges in component importance measures," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 123-130.
    4. Si, Shubin & Levitin, Gregory & Dui, Hongyan & Sun, Shudong, 2013. "Component state-based integrated importance measure for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 75-83.
    5. Huseby, Arne B. & Natvig, Bent, 2013. "Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 186-198.
    6. Claudio M Rocco S & Juan Carlos Ruiz, 2012. "Assessing the importance of components in a system modeled as a network," Journal of Risk and Reliability, , vol. 226(5), pages 464-475, October.
    7. Lisnianski, Anatoly & Frenkel, Ilia & Khvatskin, Lev, 2015. "On Birnbaum importance assessment for aging multi-state system under minimal repair by using the Lz-transform method," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 258-266.
    8. Mario Hellmich & Heinz-Peter Berg, 2013. "On the construction of component importance measures for semi-Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 15-32, February.
    9. Natvig, Bent & Huseby, Arne B. & Reistadbakk, Mads O., 2011. "Measures of component importance in repairable multistate systems—a numerical study," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1680-1690.
    10. Mario Hellmich, 2018. "Component importance based on dependence measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 229-250, April.

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