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

Jan Kohout ()
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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

Mathematics, 2023, vol. 11, issue 3, 1-23

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.

Keywords: Weibull distribution; curved Weibull plot; reliability; lifetime; time to breakdown; bathtub-shaped hazard rate; material testing; strength; number of cycles to fracture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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