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Comparisons of coherent systems under the time-transformed exponential model

Author

Listed:
  • Jorge Navarro

    (Universidad de Murcia)

  • Julio Mulero

    (Universidad de Alicante)

Abstract

The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and k-out-of-n systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In this paper, we study them by assuming a time-transformed exponential model for the joint distribution of the component lifetimes. This model is equivalent to the frailty model which assumes that they are conditionally independent given a common risk parameter (which represents the common environment risk). Under this model, we obtain explicit expressions for the system reliability function and comparison results for the main stochastic orders. We obtain both expressions from minimal path sets and those from minimal survival signatures. Some aging classes and the system residual lifetime (under different assumptions) are studied as well.

Suggested Citation

  • Jorge Navarro & Julio Mulero, 2020. "Comparisons of coherent systems under the time-transformed exponential model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 255-281, March.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:1:d:10.1007_s11749-019-00656-4
    DOI: 10.1007/s11749-019-00656-4
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    References listed on IDEAS

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    1. Caramellino, Lucia & Spizzichino, Fabio, 1996. "WBF Property and Stochastical Monotonicity of the Markov Process Associated to Schur-Constant Survivial Functions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 153-163, January.
    2. Kozlova, M. & Salminen, P., 2004. "Diffusion local time storage," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 211-229, December.
    3. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    4. 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.
    5. Serkan Eryilmaz & Frank P.A. Coolen & Tahani Coolen‐Maturi, 2018. "Mean residual life of coherent systems consisting of multiple types of dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 86-97, February.
    6. Bassan, Bruno & Spizzichino, Fabio, 2005. "Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 313-339, April.
    7. Ta, Bao Quoc & Van, Chung Pham, 2017. "Some properties of bivariate Schur-constant distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 69-76.
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    Cited by:

    1. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    2. Jorge Navarro & Franco Pellerey & Julio Mulero, 2022. "On sums of dependent random lifetimes under the time-transformed exponential model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 879-900, December.

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