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Weibull Distributions and Their Applications

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Springer Handbook of Engineering Statistics

Part of the book series: Springer Handbooks ((SHB))

Abstract

Weibull models are used to describe various types of observed failures of components and phenomena. They are widely used in reliability and survival analysis. In addition to the traditional two-parameter and three-parameter Weibull distributions in the reliability or statistics literature, many other Weibull-related distributions are available. The purpose of this chapter is to give a brief introduction to those models, with the emphasis on models that have the potential for further applications. After introducing the traditional Weibull distribution, some historical development and basic properties are presented. We also discuss estimation problems and hypothesis-testing issues, with the emphasis on graphical methods. Many extensions and generalizations of the basic Weibull distributions are then summarized. Various applications in the reliability context and some Weibull analysis software are also provided.

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Abbreviations

DFR:

decreasing failure rate

IFR:

increasing failure rate

MRL:

mean residual life

WPP:

Weibull probability plot

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Authors and Affiliations

  1. Institute of Information Sciences and Technology, Massey University, Turitea Campus, Palmerston North, New Zealand

    Chin-Diew Lai

  2. Division of Mechanical Engineering, The University of Queensland, 4072, Brisbane, QLD, Australia

    D.N. Murthy

  3. Dept. of Industrial & Systems Engineering, National University of Singapore, Kent Ridge Crescent, 119 260, Singapore, Singapore

    Min Xie

Authors
  1. Chin-Diew Lai
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  2. D.N. Murthy
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  3. Min Xie
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Corresponding authors

Correspondence to Chin-Diew Lai , D.N. Murthy or Min Xie .

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Editors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers the State University of New Jersey, 96 Frelinghuysen Road, 08854, Piscataway, NJ, USA

    Hoang Pham Prof.

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Lai, CD., Murthy, D., Xie, M. (2006). Weibull Distributions and Their Applications. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_3

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  • DOI: https://doi.org/10.1007/978-1-84628-288-1_3

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