In a bending load test for brittle materials such as ceramics for spacecraft and aircraft, the stress varies over the region under tension. Therefore, a Weibull model with nonuniform stress over the test specimen is generally used. Moreover, economic factors constrain the sample size. To reduce the number of test specimens, the optimum sizes of the specimens and the optimum allocation of a given total number of samples to each size are proposed for achieving the most precise estimation of the Weibull shape parameter. To do this, we examined data on both fracture strength and location based on two competing failure modesinternal and surface cracks. We found that the recommended number of specimen sizes is two and that the larger the ratio of the volumes of the two sizes, the more precise the estimation. Moreover, having an equal number of specimens for each size results in precision close to that of the optimal allocation. Using two different specimen sizes with an equal number of specimens for each reduces both the number and total volume of specimens drastically under ASTM C-1161-94 (standard test for flexural strength of advanced ceramics) compared to a conventional "single specimen size test" without any reduction in the precision of the estimators.

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