Determination of the Weibull parameters from the mean value and the coefficient of variation of the measured strength for brittle ceramics

Abstract

Accurate estimation of Weibull parameters is an important issue for the characterization of the strength variability of brittle ceramics with Weibull statistics. In this paper, a simple method was established for the determination of the Weibull parameters, Weibull modulus m and scale parameter 0  , based on Monte Carlo simulation. It was shown that an unbiased estimation for Weibull modulus can be yielded directly from the coefficient of variation of the considered strength sample. Furthermore, using the yielded Weibull estimator and the mean value of the strength in the considered sample, the scale parameter 0  can also be estimated accurately.

Description of the statistical variations of the measured strength for brittle ceramics: A comparison between two-parameter Weibull distribution and normal distribution

“…Empirical PDFs of: a) normalized c v and b) normalized m eslus, m tr , which is consistent with the previous studies[19,20,25]. On the other hand, although a slight increasing tendency with increasing m tr was observed for the coefficient of variation c v , all the curves shown inFig.…”

“…As a supplement to the previous studies, the present study will report a comprehensive comparison of the applicabilities between Weibull distribution and normal distribution based on Monte-Carlo simulations, with a special emphasis on the accuracy of the prediction of the stress level corresponding to a given fracture probability. Previous studies based on Monte-Carlo simulations [21,25] have confirmed that, for a given strength sample, the estimated values of Weibull parameters m and σ 0 can be determined directly and accurately with the average value and the standard deviation of the sample, implying that a sample of strength data following a Weibull distribution may also be well described with a normal distribution and vice versa. This is the main reason why we select both Weibull distribution and normal distribution as the study subjects.…”

“…2 can give only the estimated values of m and σ 0 . Therefore, Monte-Carlo simulations were frequently employed to explore the differences between the estimated values of the Weibull parameters and their true values [19][20][21][22][23][24][25][26]. It should be pointed out that, either the experimental examinations or the Monte-Carlo simulations, most of the previous studies concerning the Weibull analyses of strength variations for brittle materials were conducted based on a prerequisite that the measured strength really follows a Weibull distribution.…”

A Simple Estimation Method of Weibull Modulus and Verification with Strength Data

“…In 1989, van der Zweig [28] presented the same Robinson relation, but without citing prior works [11,16,26]. Three more approximate expressions have been published by [29][30][31] as follows (in the order of appearance):…”

Simulation on Potassium Ion Concentration Profile of Engineered Stress Profile Glass by FDTD Method

“…This phenomenon is caused by various flaws types, flaw positions and extension rates of flaws [1][2] . Naturally, strength of brittle materials is typically characterized by using statistical distribution functions (Weibull statistics) [3][4] .…”