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The Failure Rates of Mixtures

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Advances in Distribution Theory, Order Statistics, and Inference

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Mixtures of distributions of lifetimes occur in many settings. In engineering applications, it is often the case that populations are heterogeneous, often with a small number of subpopulations. In survival analysis, selection effects can often occur. The concept of a failure rate in these settings becomes a complicated topic, especially when one attempts to interpret the shape as a function of time. Even if the failure rates of the subpopulations of the mixture have simple geometric or parametric forms, the shape of the mixture is often not transparent.

Recent results, developed by the author (with Joe, Li, Mi, Savits, and Wondmagegnehu) in a series of papers, are presented. These results focus on general results concerning the asymptotic limit and eventual monotonicity of a mixture, and also the overall behavior for mixtures of specific parametric families.

An overall picture is given of different things that influence the behavior of the failure rate of a mixture.

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Author information

Authors and Affiliations

  1. University of Pittsburgh, Pittsburgh, PA, USA

    Henry W. Block

Authors
  1. Henry W. Block
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

  2. Department of Economics, University of Cantabria, s/n Avenida de los Castros, Santander, 39005, Spain

    José María Sarabia  & Enrique Castillo  & 

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© 2006 Birkhäuser Boston

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Block, H.W. (2006). The Failure Rates of Mixtures. In: Balakrishnan, N., Sarabia, J.M., Castillo, E. (eds) Advances in Distribution Theory, Order Statistics, and Inference. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4487-3_17

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