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Reduction in mean residual life in the presence of a constant competing risk

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  • Mark Bebbington
  • Chin‐Diew Lai
  • Ričardas Zitikis

Abstract

The addition of a constant ‘competing risk’ corresponding to an additional, usually less significant, source of failure, frequently improves the fit in reliability and survival analysis. This is often termed a ‘lift’, as the effect is to increase the hazard rate (HR) function by a constant, which does not, of course, change the shape and hence the turning points of the HR function. However, lifting the HR function does not, in general, mean lowering the corresponding mean residual life (MRL) function by a constant, and so the MRL turning points, unlike those of the HR function are not invariant. The MRL turning points are used in, for example, defining burn‐in procedures in reliability engineering, and determining premiums in insurance. Hence, it is of interest to examine the changes in the shape of the MRL function, and in the locations of its turning points, resulting from a lift in the HR function. We discuss these problems in detail, with reference to a number of common distributions in reliability and mortality modeling. Copyright © 2007 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmbi:v:24:y:2008:i:1:p:51-63
    DOI: 10.1002/asmb.693
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    Cited by:

    1. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    2. 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.
    3. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    4. C. Satheesh Kumar & S. Dharmaja, 2014. "On some properties of Kies distribution," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 97-122, April.
    5. MARK BEBBINGTON & CHIN-DIEW LAI & RIcARDAS ZITIKIS, 2011. "Modelling Deceleration in Senescent Mortality," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(1), pages 18-37.
    6. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.

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