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Joint distribution of a random sample and an order statistic: A new approach with an application in reliability analysis

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  • Bayramoglu, Ismihan

Abstract

This paper considers the joint distribution of elements of a random sample and an order statistic of the same sample. The motivation for this work stems from the important problem in reliability analysis, to estimate the number of inspections we need in order to detect failed components in a coherent system. We consider an (n−r+1)-out-of-n system, which is intact until at least n−r+1 of the components are alive, and it fails if the number of failed components exceeds r. The (n−r+1)-out-of-n system is a preferred type of redundancy of fault-tolerant systems used in reliability engineering and finds wide applications in industrial and military systems. Well-known examples of this system are multiengine systems in airplane, multipump systems in hydraulic control, multicylinder engines in automobile, the radar systems, communication systems with multiple transmitters, a web host with several servers. The lifetime of the system is the rth order statistic. Assuming that some of the components failed but the system is still functioning, using the results presented in this paper it is possible to find an expected value of the number of inspections we need to do for detecting certain number of failed components.

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  • Bayramoglu, Ismihan, 2020. "Joint distribution of a random sample and an order statistic: A new approach with an application in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:reensy:v:193:y:2020:i:c:s0951832019302157
    DOI: 10.1016/j.ress.2019.106594
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    References listed on IDEAS

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    1. Raqab, Mohammad Z., 2010. "Evaluations of the mean residual lifetime of an m-out-of-n system," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 333-342, March.
    2. P. Samadi & M. Rezaei & M. Chahkandi, 2017. "On the residual lifetime of coherent systems with heterogeneous components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 69-82, January.
    3. Eryilmaz, Serkan, 2013. "On reliability analysis of a k-out-of-n system with components having random weights," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 41-44.
    4. Zhang, Zhengcheng & Yang, Yonghong, 2010. "Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 711-717, April.
    5. 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.
    6. Ling, Xiaoliang & Wei, Yinzhao & Si, Shubin, 2019. "Reliability optimization of k-out-of-n system with random selection of allocative components," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 186-193.
    7. M. Poursaeed, 2010. "A note on the mean past and the mean residual life of a (n − k + 1)-out-of-n system under multi monitoring," Statistical Papers, Springer, vol. 51(2), pages 409-419, June.
    8. 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.
    9. 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.
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    Cited by:

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