Effects of the number of testing specimens and the estimation methods on the Weibull parameters of solid catalysts

• Published in: Chemical engineering science Vol. 56; no. 24; pp. 7035 - 7044
• Main Authors: Wu, Dongfang, Li, Yongdan, Zhang, Jianpo, Chang, Liu, Wu, Dihua, Fang, Zhiping, Shi, Yahua
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-12-2001; Elsevier
• Subjects: Catalysis; Catalysts: preparations and properties; Chemistry; Dispersion; Estimation precision; Exact sciences and technology; General and physical chemistry; Materials; Mechanical strength measurement; Safety; Simulation; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; Safety; Mechanical strength measurement; Estimation precision; Simulation; Dispersion; Materials; Monte Carlo method; Statistical parameter; Linear regression; Theoretical study; Mechanical properties; Numerical simulation; Maximum likelihood; Weibull distribution; Catalyst; Strength
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/S0009-2509(01)00340-2

A Monte Carlo simulation is used to obtain the statistical properties of the Weibull parameters estimated by the linear regression, weighted linear regression and maximum likelihood schemes, respectively. Results reveal that the natural logarithm of the Weibull size parameter can be determined with about the same precision as the Weibull modulus. For Weibull modulus estimation, a maximum likelihood method results in the highest estimation precision; however, with a low safety factor. The weighted linear regression method with a weight factor
W
i
=
F
i
2 and a probability estimator
P
f
(
F
i
)=(
i−0.3)/(
n+0.4) or
P
f
(
F
i
)=(
i−3/8)/(
n+1/4), which leads to a similar estimation precision and a much higher safety factor, is considered to be the best method for engineering design. Simulations show that the weight factors and the probability estimators have effects on the estimation precision. It is also concluded that the precision of any estimation method increases with the increase of the sample size. It is reaffirmed that 30–60 specimens are required to obtain a reasonable estimation precision of the Weibull parameters.