On Representing the Mean Residual Life in Terms of the Failure Rate

Details On Representing the Mean Residual Life in Terms of the Failure Rate On Representing the Mean Residual Life in Terms of the Failure Rate

2004-11-12

arxiv.org/abs/math/0411297v1

Mathematical and Computer Modelling, Vol. 37 (2003), no. 12--13, pp. 1271--1280. MR1996036 (2004e:62181)

Mathematics

Statistics Theory

10 pages

Scientific paper

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem--namely that of expressing the mean residual life in terms of the failure rate--typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.

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