Abstract
Generalized stepwise structural models of multi-modal Weibull distribution functions have been established for the bending strength of ceramics. The maximum likelihood estimators of the Weibull parameters for each model were obtained by Nelder-Mead method. By using Akaike's information criteria (AIC), a mono-modal model was selected as the most suitable one for two kinds of bending test data on steatite ceramics. However, it was pointed out that some additional data such as diagnostics data and/or additional strength data were needed.
The direct and the two-step maximum likelihood methods have been applied to Monte Carlo simulation data of the bi-modal Weibull distribution function for small sample size. The standard deviation and the mean squared error of the maximum likelihood estimators by the two-step method were two or three figures smaller than those of the direct method.
