Demonstration of the Robustness of Maximum Likelihood Estimation to Distinguish Mixtures of Two Weibull Populations in Failure Data of Brittle Materials

Abstract

In statistical analysis of failure data of brittle materials, the use of maximum likelihood estimators shows many advantages compared to other methods. The applicability and the robustness of the maximum likelihood method to analyze and to distinguish the data in several mixtures of two Weibull populations is demonstrated in this work. Estimations of percentage of data belonging to each of the populations, as well as Weibull parameters of the populations, are relatively simple to be conducted using adequate software.