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

2008 ◽  
Vol 3 (3) ◽  
pp. 155892500800300 ◽  
Author(s):  
Béchir Azzouz ◽  
Mohamed Ben Hassen ◽  
Faouzi Sakli
Keyword(s):  
Standard Deviation ◽  
Normal Distribution ◽  
Cotton Fiber ◽  
Fiber Length ◽  
Length Distribution ◽  
Binary Blends ◽  
Fiber Length Distribution ◽  
The Mean ◽  
Normal Law ◽  
Normal Fiber

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.

Bias Reduction in Kernel Estimation of the Density Function of Cotton Fiber Length

2012 ◽  
Vol 627 ◽  
pp. 23-28
Author(s):  
Yu Heng Su ◽  
Guang Song Yan
Keyword(s):  
Density Function ◽  
Cotton Fiber ◽  
Fiber Length ◽  
Length Distribution ◽  
Estimation Method ◽  
Kernel Estimation ◽  
Short Fiber ◽  
Bias Reduction ◽  
Theoretical Research ◽  
Fiber Length Distribution

Abstract. The non-parameter kernel estimation has become a dramatic method on fitting the distribution density function of cotton fiber length in theoretical research on fiber length. It can get a differentiable and integrable density function of cotton length distribution, and make the probability approach more effective on analysis and prediction of yarn performance. But, due to the requirements of the fitting smoothness, there is a bias between calculational index and measured value, especially to the short fiber content. This research uses the power function to fit the distribution of short fibers, then according to the principle of mixed distribution, revises the density function gotten by kernel estimation method, and gives a precise estimation of density function. The revised algorithm is more exact to fit the density function of fiber length. This approach is a new way to study the fiber length distribution and its effect on yarn properties both theoretically and practically.

Study on the Characterization of Cotton Fiber Length Distribution

2013 ◽  
Vol 821-822 ◽  
pp. 398-401 ◽  
Author(s):  
Xue Qin Kuang ◽  
Jian Ping Yang ◽  
Chong Wen Yu
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Cotton Fiber ◽  
Fiber Length ◽  
Mixed Model ◽  
Length Distribution ◽  
Length Frequency ◽  
Fiber Length Distribution ◽  
Two Component

In order to characterize cotton fiber length distribution, the probability density function with parameters were used to describe the fiber length frequency histograms. In this paper, four cotton fiber samples (bale, carded sliver, combed sliver and finisher sliver) were selected, and the fiber histograms by weight were measured by USTER AFIS Pro. Two- and three-component mixed Weibull distributions were adopted by us to fit these histograms, and the relevant fiber length measures were calculated. The results showed that mixed model could well describe the entire fiber length distribution of different cotton fiber samples, and two-component mixed Weibull distribution, rather than three-component one, fitted these histograms better.

Mathematical Aspects of Cotton Fiber Length Distribution under Various Breakage Models

1964 ◽  
Vol 34 (4) ◽  
pp. 303-307 ◽  
Author(s):  
Harold N. Shapiro ◽  
Gerson Sparer ◽  
Harry E. Gaffney ◽  
Russell H. Armitage ◽  
John D. Tallant
Keyword(s):  
Cotton Fiber ◽  
Fiber Length ◽  
Length Distribution ◽  
Fiber Length Distribution

Estimation of yarn strength based on critical slipping length and fiber length distribution

2017 ◽  
Vol 89 (2) ◽  
pp. 182-194 ◽  
Author(s):  
Zhan Jiang ◽  
Chongwen Yu ◽  
Jianping Yang ◽  
Guangting Han ◽  
Mingjie Xing
Keyword(s):  
Fiber Length ◽  
Length Distribution ◽  
Probability Method ◽  
Yarn Strength ◽  
Fiber Length Distribution ◽  
Yarn Twist ◽  
Twist Multiplier ◽  
Strength Based ◽  
Breaking Mechanism ◽  
Yarn Structure

Yarn strength is composed of the total contributions made by all breaking and slipping fibers which are determined by critical slipping length lc. Though the definition of lc has been the focus of many research projects, it still remains unsolved. In this study, idealized assumptions were made on yarn structure, and lc was then estimated. At the same time, the actual contributions that breaking fibers and slipping fibers make to yarn strength were recalculated based on an idealized yarn structure, which was analyzed with the conditional probability method according to fiber length distribution. Then, yarn strength was computed by simulating random fiber arrangement in the yarn. It could be seen from calculated results that the critical slipping length declines as yarn twist multiplier increases. Meanwhile, as the twist multiplier increases, the calculated yarn strength rises to the highest point and then declines, which is in agreement with traditional spinning theory. Thus, the calculation of yarn strength based on critical slipping length could reflect the yarn breaking mechanism with a change in the yarn twist multiplier, and could be applied for further prediction of yarn strength.

scholarly journals An alternative to the rejection of observations

1932 ◽  
Vol 137 (831) ◽  
pp. 78-87 ◽  
Keyword(s):  
Standard Deviation ◽  
Continuous Function ◽  
Large Deviations ◽  
Opposite Direction ◽  
Standard Error ◽  
The Other ◽  
Cause Of Error ◽  
The Mean ◽  
Normal Law ◽  
Usual Rule

1. It is widely felt that any method of rejecting observations with large deviations from the mean is open to some suspicion. Suppose that by some criterion, such as Peirce’s and Chauvenet’s, we decide to reject observations with deviations greater than 4 σ, where σ is the standard error, computed from the standard deviation by the usual rule; then we reject an observation deviating by 4·5 σ, and thereby alter the mean by about 4·5 σ/ n , where n is the number of observations, and at the same time we reduce the computed standard error. This may lead to the rejection of another observation deviating from the original mean by less than 4 σ, and if the process is repeated the mean may be shifted so much as to lead to doubt as to whether it is really sufficiently representative of the observations. In many cases, where we suspect that some abnormal cause has affected a fraction of the observations, there is a legitimate doubt as to whether it has affected a particular observation. Suppose that we have 50 observations. Then there is an even chance, according to the normal law, of a deviation exceeding 2·33 σ. But a deviation of 3 σ or more is not impossible, and if we make a mistake in rejecting it the mean of the remainder is not the most probable value. On the other hand, an observation deviating by only 2 σ may be affected by an abnormal cause of error, and then we should err in retaining it, even though no existing rule will instruct us to reject such an observation. It seems clear that the probability that a given observation has been affected by an abnormal cause of error is a continuous function of the deviation; it is never certain or impossible that it has been so affected, and a process that completely rejects certain observations, while retaining with full weight others with comparable deviations, possibly in the opposite direction, is unsatisfactory in principle.

Strength of short fiber reinforced polymers: Effect of fiber length distribution

2008 ◽  
Vol 29 (6) ◽  
pp. 644-648 ◽  
Author(s):  
Muratahan Aykol ◽  
Nihat Ali Isitman ◽  
Emre Firlar ◽  
Cevdet Kaynak
Keyword(s):  
Fiber Length ◽  
Length Distribution ◽  
Short Fiber ◽  
Fiber Reinforced Polymers ◽  
Fiber Reinforced ◽  
Reinforced Polymers ◽  
Fiber Length Distribution
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