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The Barlow-Proschan importance and its generalizations with dependent components

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  • Iyer, Srinivas

Abstract

For a coherent system the Barlow-Proschan measure of importance of component i, defined when the components are independent to be the probability that i causes system failure, will here be generalized to the case where the component lifetimes are jointly absolutely continuous but not necessarily independent. When the system has a modular decomposition, properties analogous to that of the Barlow-Proschan measure are proved. Xie has generalized the Barlow-Proschan importance using the system yield function when all components are independent. This will be extended here to dependent components.

Suggested Citation

  • Iyer, Srinivas, 1992. "The Barlow-Proschan importance and its generalizations with dependent components," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 353-359, September.
    • Handle: RePEc:eee:spapps:v:42:y:1992:i:2:p:353-359
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    Citations

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    Cited by:

    1. Marichal, Jean-Luc, 2014. "Subsignatures of systems," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 226-236.
    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. Cao, Yingsai & Lu, Chen & Dong, Wenjie, 2024. "Importance measures for multi-state systems with multiple components under hierarchical dependences," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    4. H. Metatla & M. Rouainia, 2022. "Functional and dysfunctional analysis of a safety instrumented system (SIS) through the common cause failures (CCFs) assessment. Case of high integrity protection pressure system (HIPPS)," 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. 13(4), pages 1932-1954, August.
    5. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.
    6. Emilio De Santis & Yaakov Malinovsky & Fabio Spizzichino, 2021. "Stochastic Precedence and Minima Among Dependent Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 187-205, March.
    7. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 48-56.
    8. da Costa Bueno, Vanderlei & de Menezes, Jose Elmo, 2007. "Pattern's reliability importance under dependence condition and different information levels," European Journal of Operational Research, Elsevier, vol. 177(1), pages 354-364, February.

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