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Ageing Characteristics of the Weibull Mixtures

Published online by Cambridge University Press:  27 July 2009

Pushpa L. Gupta  and
Ramesh C. Gupta
Pushpa L. Gupta
Affiliation:
Department of Mathematics & Statistics, University of Maine Orono, Maine 04469-5752
Ramesh C. Gupta
Affiliation:
Department of Mathematics & Statistics, University of Maine Orono, Maine 04469-5752
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It is well known that mixtures of decreasing failure rate (DFR) distributions have the DFR property. A similar result is, of course, not true for increasing failure rate (IFR) distributions. In a recent note, Gurland and Sethuraman (1994, Technometrks36(4): 416–418) presented two examples where mixtures of IFR distributions show DFR property. In this paper, we present a general approach to study the mixtures of distributions and show that the failure rates of the unconditional and conditional distributions cross at most at one point. Mixtures of Weibull distribution with a shape parameter greater than 1 are examined in detail. This also enables us to study the monotonic properties of the mean residual life function of the mixture. Some examples are provided to illustrate the results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 4 , October 1996 , pp. 591 - 600
Copyright
Copyright © Cambridge University Press 1996

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