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Ageing characteristics of the Weibull mixtures. (English) Zbl 1095.60509

Summary: 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, J. Gurland and J. Sethuraman [Technometrics 36, No. 4, 416–418 (1994; Zbl 0825.62722)] 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 failue 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.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
62N05 Reliability and life testing

Citations:

Zbl 0825.62722
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References:

[1] DOI: 10.2307/2347295
[2] DOI: 10.1007/BF00050672 · Zbl 0695.62223
[3] DOI: 10.1214/aoap/1177005583 · Zbl 0762.62031
[4] DOI: 10.1002/sim.4780071105
[5] DOI: 10.1007/BF02613681 · Zbl 0775.62276
[6] Cox, Journal of the Royal Statistical Society 34 pp 187– (1972)
[7] DOI: 10.2307/1269957 · Zbl 0825.62722
[8] DOI: 10.1109/24.273591 · Zbl 0799.60086
[9] DOI: 10.1080/15326349508807340 · Zbl 0813.60081
[10] DOI: 10.2307/2287666 · Zbl 0497.62017
[11] Cox, Analysis of survival data (1984)
[12] DOI: 10.2307/1269006 · Zbl 0717.62048
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