Estimation of Weibull parameters for the flexural strength of PMMA-based bone cements

Abstract

The wide scatter of data observed in the strength of bone cements based on poly(methyl methacrylate) (PMMA) can be described properly by the two-parameter Weibull function. However, the statistical character of the distribution leads to an uncertainty in the parameters evaluated from a limited number of experiments. This study is concerned with the analysis of the methods of estimation as well as sample size on the estimates of the Weibull parameters. The maximum likelihood method, moments method, and linear regression method were studied. Monte Carlo simulations were carried out in order to assess the influence of the number of specimens tested on the Weibull parameters calculated by the different methods. The number of specimens tested displayed a large influence upon the calculated Weibull modulus. By applying weighing factors to the linear regression method, the standard deviation of Weibull parameters decreased significantly. As a compromise between minimizing both the dispersion of the evaluation method and the experimental effort, the use is suggested of the linear regression method with a minimum number of 20 specimens in a nonweighted analysis and 10 in a weighted analysis.