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Textile Research Journal
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Statistics for the Number of Fiber Ends in a Segment of a Random Assembly of Aligned Fibers

G.H. Brown

CSIRO Division of Mathematics and Statistics, Lindfield, NSW 2070, Australia

Nhan G. Ly

CSIRO Division of Textile Physics, Ryde, NSW 2112, Australia

A plausible model is used to derive formulas for the expected number of fibers with zero, one, or two ends in a given length segment of a random assembly of aligned fibers. These results are then combined to form the expectation of the number of ends and various related quantities. By making a stronger assumption, an expression for the variance of the number of ends is found. A numerical illustration is used to show how the variance depends on the length of the segment involved. Various definitions for the proportion of ends are given and discussed. A brief discussion of the relevance of these results to the study of the mechanics of staple fiber yarns is included.

Textile Research Journal, Vol. 55, No. 4, 206-210 (1985)
DOI: 10.1177/004051758505500402
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