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On conditional residual lifetime and conditional inactivity time of k-out-of-n systems

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  • Tavangar, Mahdi
  • Bairamov, Ismihan

Abstract

In designing structures of technical systems, the reliability engineers often deal with the reliability analysis of coherent systems. Coherent system has monotone structure function and all components of the system are relevant. This paper considers some particular models of coherent systems having identical components with independent lifetimes. The main purpose of the paper is to study conditional residual lifetime of coherent system, given that at a fixed time certain number of components have failed but still there are some functioning components. Different aging and stochastic properties of variables connected with the conditional residual lifetimes of the coherent systems are obtained. An expression for the parent distribution in terms of conditional mean residual lifetime is provided. The similar result is obtained for the conditional mean inactivity time of the failed components of coherent system. The conditional mean inactivity time of failed components presents an interest in many engineering applications where the reliability of system structure is important for designing and constructing of systems. Some illustrative examples with given particular distributions are also presented.

Suggested Citation

  • Tavangar, Mahdi & Bairamov, Ismihan, 2015. "On conditional residual lifetime and conditional inactivity time of k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 225-233.
    • Handle: RePEc:eee:reensy:v:144:y:2015:i:c:p:225-233
    DOI: 10.1016/j.ress.2015.06.020
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    2. Saberzadeh, Zahra & Razmkhah, Mostafa & Amini, Mohammad, 2023. "Bayesian reliability analysis of complex k-out-of-n: â„“ systems under degradation performance," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
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    7. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    8. Davies, Katherine & Dembińska, Anna, 2024. "On the residual lifetimes of dependent components upon system failure," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    9. 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.
    10. Ensiyeh Nezakati & Mostafa Razmkhah & Firoozeh Haghighi, 2019. "Reliability analysis of a k-out-of-n:F system under a linear degradation model with calibrations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 537-552, June.

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