Adjustment of Cotton Fiber Length by the Statistical Normal Distribution: Application to Binary Blends

Abstract

In this study the normality of the cotton fiber length number distribution and weight distribution are tested by using the Chi-2 statistic test. Good correlations between the cotton fiber length distribution by weight and the normal distribution with the same mean and standard deviation are obtained. This test further shows that length distribution by numbers cannot be characterized by normal law. Then, the staple diagram and the fibrogram by weight are mathematically generated from a normal fiber length distribution. After that, mathematical models relating the most common length parameters to the mean length and the coefficient of variation are established by solving the staple diagram and the fibrogram equations. Finally, the length parameters of binary blends are studied and their variations in terms of the components of the blend are shown. These variations are nonlinear for most of the blend length parameters in contrast to other studies and models usually used by the spinners that suppose that the blend characteristics and particularly length parameters are linear to the components ratios.