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A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components

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  • Jorge Navarro
  • Rafael Rubio

Abstract

We give necessary and sufficient conditions based on signatures to obtain distribution‐free stochastic ordering properties for coherent systems with exchangeable components. Specifically, we consider the stochastic, the hazard (failure) rate, the reversed hazard rate, and the likelihood ratio orders. We apply these results to obtain stochastic ordering properties for all the coherent systems with five or less exchangeable components. Our results extend some preceding results. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • Jorge Navarro & Rafael Rubio, 2011. "A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 478-489, August.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:5:p:478-489
    DOI: 10.1002/nav.20463
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    References listed on IDEAS

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    1. Debasis Bhattacharya & Francisco J. Samaniego, 2010. "Estimating component characteristics from system failure‐time data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 380-389, June.
    2. 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.
    3. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    4. Mahdi Tavangar & Majid Asadi, 2010. "A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 59-73, July.
    5. Shaked, Moshe & Suarez-Llorens, Alfonso, 2003. "On the Comparison of Reliability Experiments Based on the Convolution Order," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 693-702, January.
    6. 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, December.
    7. Jorge Navarro & Marco Burkschat, 2011. "Coherent systems based on sequential order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 123-135, March.
    8. Jorge Navarro & Rafael Rubio, 2010. "Comparisons of coherent systems using stochastic precedence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 469-486, November.
    9. Shuang Li & James Lynch, 2010. "Some elementary ideas concerning the complexity of system structure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 626-633, October.
    10. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    11. Navarro, Jorge & Spizzichino, Fabio & Balakrishnan, N., 2010. "Applications of average and projected systems to the study of coherent systems," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1471-1482, July.
    12. Jorge Navarro & Moshe Shaked, 2010. "Some properties of the minimum and the maximum of random variables with joint logconcave distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 313-317, May.
    13. 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.
    14. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
    15. Xiaohu Li & Zhengcheng Zhang, 2008. "Some stochastic comparisons of conditional coherent systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 541-549, November.
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    Cited by:

    1. 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.
    2. M. Kelkinnama & M. Asadi, 2019. "Stochastic and ageing properties of coherent systems with dependent identically distributed components," Statistical Papers, Springer, vol. 60(3), pages 805-821, June.
    3. Salehi, Ebrahim & Tavangar, Mahdi, 2019. "Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 327-337.
    4. Serkan Eryilmaz, 2015. "Systems composed of two types of nonidentical and dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 388-394, August.

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