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Comparisons and bounds for expected lifetimes of reliability systems

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  • Navarro, Jorge
  • Rychlik, Tomasz

Abstract

Sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with independent and either identically or non-identically distributed lifetimes are expressed in terms of expected lifetimes of components. Similar evaluations are concluded for the respective mean residual lifetimes. In the IID case, improved inequalities dependent on a concentration parameter connected to the Gini dispersion index are obtained. The results can be used to compare systems with component lifetimes ordered in the convex ordering. In the INID case, some refined bounds are derived in terms of the expected lifetimes of series systems of smaller sizes, and the expected lifetime of single unit for the equivalent systems with IID components. The latter can be further simplified in the case of weak Schur-concavity and Schur-convexity of the system generalized domination polynomial.

Suggested Citation

  • Navarro, Jorge & Rychlik, Tomasz, 2010. "Comparisons and bounds for expected lifetimes of reliability systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 309-317, November.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:309-317
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    References listed on IDEAS

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    1. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    2. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, September.
    3. Avinash Agrawal & Richard E. Barlow, 1984. "A Survey of Network Reliability and Domination Theory," Operations Research, INFORMS, vol. 32(3), pages 478-492, June.
    4. Nickos Papadatos, 1997. "Exact Bounds for the Expectations of Order Statistics from Non-Negative Populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 727-736, December.
    5. Zhu, Y. & Elsayed, E.A. & Liao, H. & Chan, L.Y., 2010. "Availability optimization of systems subject to competing risk," European Journal of Operational Research, Elsevier, vol. 202(3), pages 781-788, May.
    6. Papageorgiou, Effie & Kokolakis, George, 2010. "Reliability analysis of a two-unit general parallel system with (n-2) warm standbys," European Journal of Operational Research, Elsevier, vol. 201(3), pages 821-827, March.
    7. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    8. Richard E. Barlow & Frank Proschan, 1976. "Theory of Maintained Systems: Distribution of Time to First System Failure," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 32-42, February.
    9. Cocozza-Thivent, Christiane, 2007. "MUT of a one out of two system with preventive maintenance," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1203-1229, November.
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