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Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties

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  • Zhengcheng Zhang
  • N. Balakrishnan

Abstract

In this paper, we present several useful mixture representations for the reliability function of the inactivity time of systems with heterogeneous components based on order statistics, signatures and mean reliability functions. Some stochastic comparisons of inactivity times between two systems are discussed. These results form nice extensions of some existing results for the case when the components are independent and identically distributed. Copyright Springer-Verlag Berlin Heidelberg 2016

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  • Zhengcheng Zhang & N. Balakrishnan, 2016. "Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 113-126, January.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:1:p:113-126
    DOI: 10.1007/s00184-015-0546-8
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    References listed on IDEAS

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    1. Navarro, Jorge & Ruiz, Jose M. & Sandoval, Carlos J., 2005. "A note on comparisons among coherent systems with dependent components using signatures," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 179-185, April.
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    5. 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.
    6. 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.
    7. 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.
    8. Parvardeh, A. & Balakrishnan, N., 2013. "Conditional residual lifetimes of coherent systems," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2664-2672.
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    Cited by:

    1. Jorge Navarro & Maria Longobardi & Franco Pellerey, 2017. "Comparison results for inactivity times of k-out-of-n and general coherent systems with dependent components," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 822-846, December.
    2. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    3. Jorge Navarro & Yolanda Águila, 2017. "Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 627-648, November.

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