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The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections

Author

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  • Zhouxia Guo

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

  • Jiandong Zhang

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

  • Rongfang Yan

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

Abstract

In this manuscript, we gain a mixture representation for reliability function of the residual lifetime of unfailed components in a coherent system under periodical inspections, given that the number of failed components before time t 1 is r ( ≥ 0 ) , but the system is still operating at time t 1 , and the system eventually failed at time t 2 ( > t 1 ) . Some aging properties and stochastic orders of the residual lifetime on survival components are also established. Finally, some numerical examples and graphs are given in order to confirm the theoretical results.

Suggested Citation

  • Zhouxia Guo & Jiandong Zhang & Rongfang Yan, 2020. "The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections," Mathematics, MDPI, vol. 8(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2181-:d:457936
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    References listed on IDEAS

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    5. 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.
    6. A. Parvardeh & N. Balakrishnan & Azam Arshadipour, 2018. "A note on the conditional residual lifetime of a coherent system under double monitoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(10), pages 2373-2378, May.
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