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Comment on "A new probability index for estimating Weibull modulus for ceramics with the least-square method"
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The Weibull distribution has been commonly used to describe the statistical variation in the fracture strength of brittle materials. Using Weibull's two-parameter equation, the probability of failure P at stress σ represented by [1] P = 1 - exp [-(σ/σ_0)~m] (1) where m and σ_0 are the Weibull modulus and scale parameter, respectively. The most widely used method to estimate the two parameters from a set of experimentally measured fracture stresses is by using linear regression (LR), involving the ranging of the strength data in an ascending order and the assignment of probability of failure to each datum [2]. There are several expressions to define the probability estimator [1]. In a letter entitled "A new probability index for estimating Weibull modulus for ceramics with the least-square method" [3], Gong proposed another one as follows: P_i = i-0.999/n=1000 (2) where n is the sample size, i.e. the number of specimens tested, and P_i is the probability of failure for the ith ranked datum. Equation 2 was recommended by the author because with correction factors used, it may result in a more accurate estimation of the Weibull modulus than the following two commonly used.
Dongfang Wu、Hong Jiang
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Research Institute of Industrial Catalysis, EAst China University of Science & Technology, Shanghai 200237
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