In this study, the dependency of the variation in the shape parameter
m, which was determined in the two-parameter Weibull distribution function fitted to a strength distribution, on the number of samples,
n, was investigated by using data in numerically simulated distributions. By random sampling, five groups, i. e. (a) forty sets of
n=5, (b) twenty sets of
n=10, (c) eight sets of
n=25, (d) five sets of
n=40, and (e) two sets of
n=100, were prepared for the present analysis.
It was clarified that the variation of
m-value was enlarged with decreasing the number of samples, and its variation range as an absolute value became larger as the shape parameter determined for the original population is increased. Values of the shape parameter, which were obtained for respective numbers of samples, were normalized by the shape parameter for the original population. By such normalization, it was revealed that a relative
m-variation with respect to the number of samples was hardly dependent on the shape parameter for the original population. The simulated behavior of
m-variation was also found to coincide with that observed in four-point bending test using a pressureless sintered alpha silicon carbide.
Finally, it should be noted that the number of samples to be used in a strength test, which is recommended in JIS, is not always enough for a better understanding of the statistical strength characteristics in ceramics.
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