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Four-Parameter Weibull Distribution with Lower and Upper Limits Applicable in Reliability Studies and Materials Testing

Author

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  • Jan Kohout

    (Department of Mathematics and Physics, Military Technology Faculty, University of Defence, Kounicova 65, CZ-662 10 Brno, Czech Republic)

Abstract

A simply curved Weibull plot means that the studied data set has a three-parameter Weibull distribution with a non-zero location parameter representing the lower or the upper limit of the data set. This paper introduces a four-parameter Weibull distribution with both of these limits that can be applied in both reliability and materials engineering. A very reliable indicator of this distribution is the double-curved Weibull plot. The great advantage of this distribution is the fact that the corresponding hazard rate curve can be bathtub-shaped with a great ability to fit the measured data.

Suggested Citation

  • Jan Kohout, 2023. "Four-Parameter Weibull Distribution with Lower and Upper Limits Applicable in Reliability Studies and Materials Testing," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:544-:d:1041577
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    References listed on IDEAS

    as
    1. Zeng, Hongtao & Lan, Tian & Chen, Qiming, 2016. "Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 307-315.
    2. Farouk Metiri & Halim Zeghdoudi & Abdelali Ezzebsa, 2022. "On the characterisation of X-Lindley distribution by truncated moments. Properties and application," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 97-109.
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