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New Results on the Barlow–Proschan and Natvig Measures of Component Importance in Nonrepairable and Repairable Systems

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  • Bent Natvig

    (University of Oslo)

  • Jørund Gåsemyr

    (University of Oslo)

Abstract

In this paper dynamic and stationary measures of importance of a component in a binary system are considered. To arrive at explicit results we assume the performance processes of the components to be independent and the system to be coherent. Especially, the Barlow–Proschan and the Natvig measures are treated in detail and a series of new results and approaches are given. For the case of components not undergoing repair it is 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. 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. 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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:4:d:10.1007_s11009-008-9079-1
    DOI: 10.1007/s11009-008-9079-1
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    References listed on IDEAS

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    1. Jørund Gåsemyr & Bent Natvig, 2005. "Probabilistic Modelling of Monitoring and Maintenance of Multistate Monotone Systems with Dependent Components," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 63-78, March.
    2. 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.
    3. Jørund Gåsemyr & Bent Natvig, 1995. "Using Expert Opinions in Bayesian Prediction of Component Lifetimes in a Shock Model," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 227-242, February.
    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. 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.

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