Influence of the sample number for the prediction of the tensile strength of high tenacity viscose fibres using a two parameters Weibull distribution

The objective of this work is to determine an adequate number of samples for an accurate prediction of tensile strength of fibres using a Weibull distribution. Theory will be compared to experimental results in order to know the effect of experimental errors on the theoretical expectations. The diameter and strength distribution of high tenacity viscose were evaluated. The chosen Weibull distribution was with two parameters. First, the best probability estimator for Weibull was determined using a random selection of experimental datas. Then, in order to be able to predict the number of sample knowing the variation of the Weibull modulus m, different relationship between the coefficient of variation of m and the number of sample n were tested. The relationship CV = 0.78/ $$\sqrt n$$ presented good agreement with experimental datas. The influence of the variation of m on the predicted value of strength was studied in order to determine an adequate number of sample to obtain limited variation of the predicted strength. The last part focus on experimental verification of the points previously developed. It was shown that it is possible to determine the influence of the variation of the Weibull modulus on the predicted strength. However, no correlation was found between the variations of the Weibull modulus and the error on the predicted strength.