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Estimation of reliability in a series system with random sample size

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  • Al-Mutairi, D.K.
  • Ghitany, M.E.
  • Gupta, Ramesh C.

Abstract

In this paper, we are interested in the estimation of the reliability coefficient R=P(X>Y), when the data on the minimum of two exponential samples, with random sample size, are available. The confidence intervals of R, based on maximum likelihood and bootstrap methods, are developed. The performance of these confidence intervals is studied through extensive simulation. A numerical example, based on a real data, is presented to illustrate the implementation of the proposed procedure.

Suggested Citation

  • Al-Mutairi, D.K. & Ghitany, M.E. & Gupta, Ramesh C., 2011. "Estimation of reliability in a series system with random sample size," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 964-972, February.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:964-972
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    References listed on IDEAS

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    1. Gupta, Ramesh C. & Peng, Cheng, 2009. "Estimating reliability in proportional odds ratio models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1495-1510, February.
    2. Gupta, Ramesh C. & Li, Xue, 2006. "Statistical inference for the common mean of two log-normal distributions and some applications in reliability," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3141-3164, July.
    3. Bartoszewicz, Jaroslaw, 2001. "Stochastic comparisons of random minima and maxima from life distributions," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 107-112, November.
    4. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
    5. D. Gupta & R. C. Gupta, 1984. "On The Distribution Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(1), pages 13-19, March.
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    1. Gupta, Ramesh C. & Ghitany, M.E. & Al-Mutairi, D.K., 2012. "Estimation of reliability in a parallel system with random sample size," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 44-55.
    2. Eryilmaz, Serkan, 2016. "A new class of lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 63-71.

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