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On the behavior and shape of mixture failure rates from a family of IFR Weibull distributions

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  • Eshetu T. Wondmagegnehu

Abstract

Populations of many types of component are heterogeneous and often consist of a small number of different subpopulations. This is called a mixture and it arises in a number of situations. For example, a majority of products in industrial populations are mixtures of defective items with shorter lifetimes and standard items with longer lifetimes. It is a well‐known result that distributions with decreasing failure rates are closed under mixture. However, mixtures of distributions with increasing failure rates are not easily classifiable. If the subpopulations involved in the mixture have increasing failure rates, there might be some upward movement in the mixture and later a general downward pull towards the strongest component. Little work has been done in describing the shape of mixture failure rates when all subpopulations do not have decreasing failure rate. In this paper, we present general results that describe the shape and behavior of a failure rate of a mixture obtained from two Weibull subpopulations with strictly increasing failure rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • Eshetu T. Wondmagegnehu, 2004. "On the behavior and shape of mixture failure rates from a family of IFR Weibull distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 491-500, June.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:4:p:491-500
    DOI: 10.1002/nav.20009
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    References listed on IDEAS

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    1. R. Jiang & D. N. P. Murthy, 1998. "Mixture of Weibull distributions—parametric characterization of failure rate function," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 47-65, March.
    2. Jie Mi, 1996. "Limiting behavior of mixtures of discrete lifetime distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 365-380, April.
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    Cited by:

    1. Maxim Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 643-663, November.

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