Based on minimum mean square error, a modified probability estimator is proposed by a Monte Carlo simulation for estimating the Weibull parameters with the linear regression method. It is shown that compared with the commonly used estimators, the modified probability estimator gives a more accurate estimation of the Weibull modulus and the same estimation precision of the scale parameter. Furthermore, it is more conservative than the commonly used estimator recommended by previous authors and hence results in a higher safety in reliability predictions.
‘Standard practice for reporting uniaxial strength data and estimating Weibull distribution parameters for advanced ceramics’, ASTM standard C1239-00, ASTM International, Philadelphia, PA, USA, 2000.
2.
QuinnG. D.: J. Am. Ceram. Soc., 1990, 73, 2374–2384.
3.
PapargyrisA. D.: J. Eur. Ceram. Soc., 1998, 18, 451–455.
4.
KhaliliA. and KrompK.: J. Mater. Sci., 1991, 26, 6741-6752.
5.
BergmanB.: J. Mater. Sci Lett., 1984, 3, 689–692.
6.
SullivanJ. D. and LauzonP. H.: J. Mater. Sci. Lett., 1986, 5, 1245–1247.
7.
LangloisR.: J. Mater. Sci. Lett., 1991, 10, 1049–1051.
8.
TrustrumK. and deA.JayatilakaS.: J. Mater. Sci., 1979, 14, 1080-1084.
9.
PeterlikH.: J. Mater. Sci., 1995, 30, 1972-1976.
10.
WuD. F., ZhouJ. C. and LiY. D.: J. Mater. Set, 2006, 41, 5630–5638.
11.
D'AgostinoR. B. and StephensM. A.: ‘Goodness-of-fit techni-ques’: 1986, New York, NY, Marcel Dekker.
12.
CoxD. R. and SnellE. J.: ‘Applied statistics — principles and examples’: 1987, London, Chapman & Hall.
