Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 48--56

HOW TO MEASURE UNCERTAINTY IN THE RESIDUAL LIFE TIME DISTRIBUTION

By

NADER EBRAHIMI, Northern Illinois University

SUMMARY.  A conventional approach to characterize the life distribution of a component is by one of the well known measures, e.g., hazard rate function or mean-residual life-time function. Aging of a component is usually described either in terms of increasing hazard rate function or decreasing mean residual life time function. In this paper we propose an alternative characterization of a life distribution in terms of conditional Shannon's measure of uncertainty. That is, Shannon's information measure applied to the residual life time. Based on our proposed measure new classes of life distributions are defined which mimic the increasing failure rate and decreasing failure rate. It is shown that these new classes are different from the known classes of life distributions. Various inequalities are established in the same section.

AMS (1980) subject classification.  Primary 62N05; secondary 60E15; 90B25.

Key words and phrases. Information, entropy, IFR, DFR, IFRA, DFRA, hazard function, mean residual life function, survival function.

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