首页|Determining the confidence intervals of Weibull parameters estimated using a more precise probability estimator
Determining the confidence intervals of Weibull parameters estimated using a more precise probability estimator
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The two-parameter Weibull model [1] has been used to model the statistical variation in the failure stress of nominally identical ceramic components [2]. The probability that a given component will fracture at or below a tensile stress, σ, can be predicted as P_f = 1-exp [-(σ/σ_0)~m] (1) where m is the shape parameter, or Weibull modulus, and σ_0 is the scale parameter, or characteristic strength. The distribution parameters, m and σ_0, can be estimated by fitting Equation 1 to a random sample of n specimens with failure stresses, σ_i, and cumulative probabilities of failure, P_i, where i is the rank of each specimen. Cumulative probability of failure is usually calculated by applying a discrete probability estimator of the form [3-5] P-circumflex_i = i-α/n+β (2) where α and β are constant historically selected to minimize the bias of the sample Weibull modulus, m-cricumflex, so that m-circumflex/m≈1. Gong recently suggested the use of a correction factor, k_M= m-circumflex/k_m, may serve as an unbiased estimate of m [6]. Gong showed that values of α=-0.999 and β=1000 resulted in a low standard deviation for k_M and therefore a precise estimate of m.
J. A. Griggs、Yunlong Zhang
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Department of Biomaterials Science, Baylor College of Dentistry, Rtexas A & M University System Health Science Center, 3302 Gaston Avenue, Dallas, TX 75246, USA
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