Counting precision for spinning fineness under non-Gaussian distributions
by
Kym Butler
Agriculture Victoria
Coauthors: Angela Pezic (RMIT University), Basil de Silva (RMIT University)

Spinning fineness (Butler & Dolling (1995) Journal of Textile Institute, 86, 164-166) of wool is more closely related to later stage processing performance and fabric quality than mean fibre diameter. It provides a way of modifying mean fibre diameter so that the effect of the distribution of fibre diameters is taken into account in a manner that relates to the performance of wool. Mathematically, spinning fineness is simply a function of mean fibre diameter and the coefficient of variation of fibre diameter.

When either mean fibre diameter or spinning fineness is calculated using a direct method that is based on counting individual fibres, the number of fibres counted limits the precision. At Biometrics 1999, I presented the result that when the distribution of fibres is Gaussian, the asymptotic relative precision (ie relative to its value) of spinning fineness is only marginally worse than the relative precision of mean fibre diameter. We extend this result to more general distributions, and calculate the proportional increase in sample size needed for spinning fineness, over that needed for mean fibre diameter, to achieve the same asymptotic relative precision. The proportional increase in sample size is a function of the coefficient of variation, the coefficient of skewness and the coefficient of kurtosis. On examining commercial wool sale lot data, the proportional increase in sample size needed to maintain the same asymptotic relative precision is much greater than that found assuming a Gaussian distribution of fibre diameters.

Date received: August 30, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahg-62.