Three-parameter Weibull distribution with upper limit applicable in reliability studies and materials testing. (October 2022) - Kohout, Jan
Abstract: The Weibull plot with concave shape of an experimental curve mostly indicates the necessity to use the three-parameter Weibull distribution with nonzero location parameter, which represents the lower limit of studied data set. The paper proposes a three-parameter Weibull distribution function with the localization parameter representing the upper limit of the studied data set. This function is suitable for the Weibull plot with convex shape of experimental curve. Several examples of applying the newly proposed function are presented: for lifetime or time-to-breakdown in reliability studies and for strength properties in materials testing. Highlights: A simply curved Weibull plot can be fitted using the 3-parameter Weibull distribution. For its convex shape, 3-parameter Weibull CDF with upper limit t ∞ was proposed. Bathtub-shaped hazard curves with minimum in t min = (1 − β ) t ∞ / 2 are gained if β < 1. Maximum likelihood expression for the distribution parameter calculation was derived. New distribution applicability was well verified in reliability and material testing.