On Changes in the Weight Distribution Function of Artificial Fibers Due to Random Fiber Breakage

Abstract

It is possible to prepare artificial fibers so that each of them has, initially, the same length. This possibility simplifies the mathematical treatment of the subsequent ran dom time breakage, as in ginning. Upper and lower bounds to an exact expression for the time-dependent weight distribution function, W(l, t), are found. Under certain conditions, the bounds coalesce to the exact solution W(l, t). The usefulness of the approximations found for testing the theory and in finding cer tain transition probabilities associated with fiber decay is discussed.