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On the crossings of reliability measures

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  • Gupta, Ramesh C.
  • Gupta, Pushpa L.

Abstract

The proportional hazards model has been extensively used in the literature to model failure time data. However, there are many practical situations where, in comparing two groups or treatments, the proportional hazard assumption is not satisfied. In fact, the two hazards cross at one point or even more than one point. Generally, the survival (reliability) data are analyzed by three reliability measures viz failure rate, the survival function and the mean residual life function and theoretically these measures are equivalent, i.e. knowledge of one implies the knowledge of others. In this paper we study the crossings of the survival functions and the mean residual life functions in case the two hazards cross at one or two points. It is shown that, in both the cases, the number of crossings do not exceed the number of crossings of the hazard functions. The location of these crossings is also examined in relation to the crossings of the hazard functions.

Suggested Citation

  • Gupta, Ramesh C. & Gupta, Pushpa L., 2000. "On the crossings of reliability measures," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 301-305, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:3:p:301-305
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    References listed on IDEAS

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    1. Sheila M. Gore & Stuart J. Pocock & Gillian R. Kerr, 1984. "Regression Models and Non‐Proportional Hazards in the Analysis of Breast Cancer Survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 176-195, June.
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    Cited by:

    1. Bekker, Leonid & Mi, Jie, 2003. "Shape and crossing properties of mean residual life functions," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 225-234, September.
    2. Ibrahim Elbatal & Emrah Altun & Ahmed Z. Afify & Gamze Ozel, 2019. "The Generalized Burr XII Power Series Distributions with Properties and Applications," Annals of Data Science, Springer, vol. 6(3), pages 571-597, September.

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