Is a three-parameter Weibull function really necessary for the characterization of the statistical variation of the strength of brittle ceramics?

Systematic Monte Carlo simulations were performed in the present study to examine the effectiveness of two-parameter Weibull function in the characterization of the strength variation and fracture reliability of a material whose strength follows a three-parameter Weibull distribution. It was shown that two-parameter Weibull function is sufficiently suitable for the description of the statistical variation of the conventionally adopted small strength sample, regardless of whether the strength follows a two-parameter or a three-parameter Weibull distribution. Furthermore, for a material whose strength follows a three-parameter Weibull distribution, accurate determinations of the fracture stress corresponding to a given fracture probability may be obtained based on two-parameter Weibull analysis. Therefore, it is concluded that three-parameter Weibull function is not necessary for the analysis of the statistical variation of the fracture strength of brittle ceramics.