Comparison between Multi-Correlation Factor Method and Multi-Maximum Likelihood Method in Estimation of Parameters of Multi-Modal Weibull Distribution Function

Abstract

Sakai et al. established the “correlation factor method” for estimating 3-parameters in Weibull distribution function. However, this method can only be applied to mono-modal fracture models.
In this work, for analyzing multi-modal Weibull distribution function we suggested a new estimating method, namely the multi-correlation factor method, by employing Kaplan-Meier method which can separate the data into individual causes of fracture. By Monte Carlo simulation for bimodal Weibull distribution function (6-parameters) we compared the multi-correlation factor method with the multi-maximum likelihood method. It was concluded that the multi-maximum likelihood method was more accurate than the multi-correlation factor method. Further, we estimated six Weibull parameters for 403 data of Si₃N₄ obtained by 3-point bending tests.