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New results on stochastic comparisons of two-component series and parallel systems


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  • Misra, Neeraj
  • Misra, Amit Kumar
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    Let X1,X2, and X3 be independent random variables with absolutely continuous distributions having the common support [0,∞). We show that if X1≤hr[mrl,lr]X3 and X2≤hr[mrl,lr]X3, then max{X1,X2}≤hr[mrl,lr]max{X1,X3}. We also show that if X2≤rh[lr]X1 and X2≤rh[lr]X3, then min{X1,X2}≤rh[lr]min{X1,X3}. These results generalize and extend some of the results given in Shaked and Shanthikumar (2007, Example 1.C.36, p. 56), Joo and Mi (2010), and Da et al. (2010).

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 2 ()
    Pages: 283-290

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:283-290

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    Keywords: Hazard rate order; Likelihood ratio order; Mean residual life order; Reversed hazard rate order; Usual stochastic order;


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    1. Zhao, Peng & Balakrishnan, N., 2011. "New results on comparisons of parallel systems with heterogeneous gamma components," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 36-44, January.
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    Cited by:
    1. Ding, Weiyong & Zhang, Yiying & Zhao, Peng, 2013. "Comparisons of k-out-of-n systems with heterogenous components," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 493-502.
    2. Fang, Longxiang & Zhang, Xinsheng, 2013. "Stochastic comparisons of series systems with heterogeneous Weibull components," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1649-1653.


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