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 Wi =F2i and a probability estimator Pf(Fi)=(i−0.3)=(n+0.4) or Pf(Fi)=(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 e ects 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 rea;rmed that 30-60 specimens are required to obtain a reasonable estimation precision of the Weibull parameters.

Mathematical

The

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.

Monolithic catalysts were prepared by washcoating an alumina sol and then im pregnating Cu Mn Ag mixed oxides onto cordierite substrates. The effects of the preparation parameters including the Ag/Cu/Mn ratio, the total amount of active phase and the loading of washcoat, and the reaction conditions, e. g., the space velocity and the oxygen/toluene ratio on the catalytic performance for the corn bustion of toluene were investigated. It is shown that the Cu Mn Ag oxides are very active for the combustion of toluene and that the highest catalytic activity is achieved over a monolithic catalyst containing 14. 7wt% of washcoat and 21. 2 wt % of active phase with a Ag/Cu/Mn molar ratio of 13. 8/43. 1/43. 1. It is also seen that the optimum catalyst has a good catalytic stability and exhibits an excellent activity not only at a rather high space velocity but also within a wide range of oxygen/toluene ratios.