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On quantile reversed residual lifetime and its aging properties

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  • Mervat Mahdy
  • Ramadan Mahdy

Abstract

If the random variable T denotes the lifetime (T > 0, with probability one) of a unit, then the random variable T (t) =[t − T|T ⩽ t],, for a fixed t, is known as the inactivity time or the reversed residual lifetime. In this paper, we define a new class of life distributions based on the quantile of the random variable T( t ) and study its reliability properties. Some new results of the proposed class are demonstrated including some closure properties. In particular, the quantile reversed residual lifetime functions of some well-known life distributions are illustrated. Finally, we define a new stochastic ordering based on the quantile reversed residual lifetime and study its reliability properties and closure properties. Copyright Sapienza Università di Roma 2012

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  • Mervat Mahdy & Ramadan Mahdy, 2012. "On quantile reversed residual lifetime and its aging properties," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 121-131, August.
    • Handle: RePEc:spr:metron:v:70:y:2012:i:2:p:121-131
    DOI: 10.1007/BF03321970
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    References listed on IDEAS

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    1. Mark Bebbington & Chin‐Diew Lai & Ričardas Zitikis, 2008. "Reduction in mean residual life in the presence of a constant competing risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(1), pages 51-63, January.
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    3. Xiaohu Li & Jing Chen, 2004. "Aging properties of the residual life length of k‐out‐of‐n systems with independent but non‐identical components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(2), pages 143-153, April.
    4. Frostig, Esther, 2006. "On risk dependence and mrl ordering," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 231-243, February.
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