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Title: Obtaining Cotton Fiber Length Distribution from Beard Test Method Part 1 - Theoretical Distribution of Cotton Fiber Length )

Author
 Cui, Xiaoliang Rodgers, James Cai, Yiyun Li, Linxiong Belmasrour, Rachid Pang, Su Seng

 Submitted to: Journal of Cotton Science Publication Type: Peer Reviewed Journal Publication Acceptance Date: 9/9/2009 Publication Date: 12/31/2009 Citation: Cui, X., Rodgers III, J.E., Cai, Y., Li, L., Belmasrour, R., Pang, S. 2009. Obtaining Cotton Fiber Length Distribution from Beard Test Method Part 1 - Theoretical Distribution of Cotton Fiber Length . Journal of Cotton Science. 13:265-273. Interpretive Summary: Fiber length is considered the most important property of cotton in marketing and yarn processing. If the entire fiber length distribution is known, all length parameters (such as the average fiber length, percentage of fibers shorter than a half inch) can be calculated from it. Advanced Fiber Information System (AFIS) instrument can measure each individual fiber and report the fiber length distribution. However, it is rather slow and has been used mostly in research and quality control in textile mills. On the other hand, by testing a tapered fiber beard, certain fiber length parameters can be obtained rapidly. This study is aimed at exploring the possibility to obtain the entire length distribution of a sample from the beard test method. In Part 1, the mathematical function describing cotton fiber length was searched both for the original sample population and the fibers actually picked and measured by the beard method. Eight cotton samples with a wide range of fiber length are selected and tested on the AFIS instrument. The measured single fiber length data are used for finding the underlying theoretical distribution of the cotton. It is found that a mixture of two Weibull distributions fits the data very well. Numerical comparisons for various parameters between the original distribution from the data and the fitted distribution are presented. Part 2 will discuss the inference of fiber length distribution from beard test method. Technical Abstract: By testing a tapered fiber beard, certain fiber length parameters can be obtained rapidly. This study is aimed at exploring the possibility to obtain the entire length distribution of a sample from the beard test method. In Part 1, the mathematical function describing cotton fiber length was searched both for the original sample population and the fibers actually picked and measured by the beard method. Eight cotton samples with a wide range of fiber length are selected and tested on the Advanced Fiber Information System (AFIS) instrument. The measured single fiber length data are used for finding the underlying theoretical distribution of the cotton. The theoretical distribution can be considered as the population distribution of the cotton. It is found that a mixture of two Weibull distributions fits the data very well. Fiber length distributions by number and by weight are discussed separately, and in both cases a mix of two Weibull distributions shows a good fit to the data. Numerical comparisons for various parameters between the original distribution from the data and the fitted distribution are presented. Part 2 will discuss the inference of fiber length distribution from beard test method.