Monte Carlo simulations were used to search for the probability estimator for the unbiased estimate of the Weibull parameters in the linear regression method. Compared with commonly-used probability estimators, the estimator proposed gives a more accurate estimation of the Weibull modulus and the same estimation precision of the scale parameter. It is found that the estimator proposed is more conservative than the estimator Pi = (i−0.5)/n recommended by previous authors, and hence results in a higher safety in reliability predictions. The unbiased properties of the estimated Weibull parameters were validated with actual experimental data. It is also concluded that the estimated Weibull modulus from actual experimental data is more dispersive than that from Monte Carlo simulation, which arises from the fact that the strength data from actual experiments does not perfectly follow the Weibull statistics.

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The Taguchi method, a powerful tool to the optimization for quality, is used to improve the mechanical properties of a PCoMoAl hydrotreating catalyst in the impregnating and drying processes. An orthogonal array is selected to analyze the effects of the process factors, ie, impregnating temperature, impregnating time, drying temperature, and drying time. Through this study, not only can the main process factors that affect the mean strength and the Weibull modulus be found, but also the optimal factor levels can be obtained. Results show that the drying temperature is the most significant process factor affecting both the mean strength and the Weibull modulus. It has been shown that the mean strength, Weibull modulus, and mechanical reliability of the ydrotrating catalyst can be improved singificanuly with the optimization of the impregnating and drying process factors. Experimental results are also provided to confirm the effectiveness of the Taguchi method.