Three-Parameter vs. Two-Parameter Weibull Model for Single Fiber Strength  
Author Ningxiang Wu
Co-Author(s) Liyang Xie
Abstract Two-parameter Weibull distribution has been used widespread in fiber strength prediction since it significantly simplifies the analysis. However, prediction by the distribution is often conservative. In this paper, three-parameter Weibull distribution was conpared with two-parameter Weibull distribution not only in the goodness of fit to fiber strength data, but also in the accuracy of fiber strength prediction. It was found the average fiber strength is no longer linear with fiber length in log-log plot and two-parameter Weibull model cannot describe gauge length effects exactly if threshold stress exsists. So threeparameter Weibull distribution was used and a Quasi Maximum Likelihood Estimation (QMLE) method using the relationship between the standard deviation of fiber strength and fiber length was proposed for parameter estimation. The method was test by both simulation data and experimental data from open literature.
Keywords fiber strength, Weibull distribution, gauge length effects, parameter estimation
    Article #:  23-234
Proceedings of the 23rd ISSAT International Conference on Reliability and Quality in Design
August 3-5, 2017 - Chicago, Illinois, U.S.A.