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Measures of component importance in repairable multistate systems—a numerical study

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  • Natvig, Bent
  • Huseby, Arne B.
  • Reistadbakk, Mads O.

Abstract

Dynamic and stationary measures of importance of a component in a repairable multistate system are an important part of reliability. For multistate systems little has been published until now on such measures even in the nonrepairable case. According to the Barlow–Proschan type measures a component is important if there is a high probability that a change in the component state causes a change in whether or not the system state is above a given state. On the other hand, the Natvig type measures focus on how a change in the component state affects the expected system uptime and downtime relative to the given system state. In the present paper we first review these measures which can be estimated using advanced simulation methods. Extending earlier work from the binary to the multistate case, a numerical study of these measures is then given for two three component systems, a bridge system and also applied to an offshore oil and gas production system. In the multistate case the importance of a component is calculated separately for each component state. Thus it may happen that a component is very important at one state, and less important, or even irrelevant at another. Unified measures combining the importances for all component states can be obtained by adding up the importance measures for each individual state. According to these unified measures a component can be important relative to a given system state but not to another. It can be seen that if the distributions of the total component times spent in the non-complete failure states for the multistate system and the component lifetimes for the binary system are identical, the Barlow–Proschan measure to the lowest system state simply reduces to the binary version of the measure. The extended Natvig measure, however, does not have this property. This indicates that the latter measure captures more information about the system.

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  • 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.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:12:p:1680-1690
    DOI: 10.1016/j.ress.2011.07.006
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    References listed on IDEAS

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    1. Ramirez-Marquez, Jose Emmanuel & Coit, David W., 2007. "Multi-state component criticality analysis for reliability improvement in multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1608-1619.
    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. 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.
    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.
    5. Zio, Enrico & Marella, Marco & Podofillini, Luca, 2007. "Importance measures-based prioritization for improving the performance of multi-state systems: application to the railway industry," Reliability Engineering and System Safety, Elsevier, vol. 92(10), pages 1303-1314.
    6. Ramirez-Marquez, Jose E. & Rocco, Claudio M. & Gebre, Bethel A. & Coit, David W. & Tortorella, Michael, 2006. "New insights on multi-state component criticality and importance," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 894-904.
    7. 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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    Cited by:

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    3. 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.
    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.

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