Journal Article Application of a truncated distribution for tsumugi yarn width

Sakaguchi, Akio  ,  Yasuhara, Koji  ,  Kimura, Hirokazu

85 ( 9 )  , pp.929 - 935 , 2015-06 , SAGE PUBLICATIONS LTD
Hand-spun, silk yarn made from floss silk is referred to as tsumugi yarn. It gives a unique appearance on the products, also called tsumugi, which are considered to be an important type of fabric for their aesthetics. The essential factor of this visual effect is originated by the thickness variation of tsumugi yarn; however, the detail of the variation is unknown. In this paper, as a fundamental study of tsumugi yarn, its width distribution is discussed. To model the width distribution, the Polya-Eggenberger distribution is introduced. Moreover some modifications are applied for the distribution to describe the yarn's situation. That is to say, it is impossible to be thinner than a level of thickness for the yarn to maintain a shape of a thread; on the other hand, tsumugi yarn is not limited to only containing thicker parts. Additionally, it is unavoidable to involve errors and fluctuations in the actual data. Hence, the distribution is truncated and convoluted. By using an image scanner, the width of tsumugi yarn is measured. With the measured data, the parameters of the width distribution are estimated using the maximum likelihood method. The results show that the width distribution of tsumugi yarn is asymmetric and well summarized by the distribution.

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