The Distribution of Cotton Fiber Length

By testing a fiber beard, certain cotton fiber length parameters can be obtained rapidly. This is the method used by the High Volume Instrument (HVI). This study is aimed to explore the approaches and obtain the inference of length distributions of HVI beard samples in order to develop new methods that can help us find the distribution of original fiber lengths and further improve HVI length measurements. At first, the mathematical functions were searched for describing three different types of length distributions related to the beard method as used in HVI: cotton fiber lengths of the original fiber population before picked by the HVI Fibrosampler, fiber lengths picked by HVI Fibrosampler, and fiber beard's projecting portion that is actually scanned by HVI. Eight sets of cotton samples with a wide range of fiber lengths are selected and tested on the Advanced Fiber Information System (AFIS). The measured single fiber length data is used for finding the underlying theoretical length distributions, and thus can be considered as the population distributions of the cotton samples. In addition, fiber length distributions by number and by weight are discussed separately. In both cases a mixture of two Weibull distributions shows a good fit to their fiber length data. To confirm the findings, Kolmogorov-Smirnov goodness-of-fit tests were conducted. Furthermore, various length parameters such as Mean Length (ML) and Upper Half Mean Length (UHML) are compared between the original distribution from the experimental data and the fitted distributions. The results of these obtained fiber length distributions are discussed by using Partial Least Squares (PLS) regression, where the distribution of the original fiber length from the distribution of the projected one is estimated. Finally, reducing the number of parameters in a regression can enhance the estimation of parameters. To this end we introduced a new distribution with only three parameters to describe the distribution of fiber lengths by weight.;Keywords. Fiber Beard, Komogorov-Simirnov goodness-of-fit test, Mixture of Weibull Distributions, Partial Least Squares.