A Probability Model for Random Fiber Breakages

Abstract

Applications of the probability model for random fiber breakage which was derived in Part I are demonstrated. The parameters of the model for an arbitrary initial fiber- length distribution are estimated by the nonlinear least-squares iterative method. Some practical uses of the estimates of parameters are shown. Different modes of fiber break age for two different lots of cotton due to opening-carding process are assessed in terms of average number of break points and probability of fiber breakage, thus, providing complete clarification to the fundamental questions raised at the beginning of the study and a realistic interpretation to the random fiber breakage phenomena. Results of the application show that the probability of fiber breakage on fiber length is moderately nonlinear and sizable three segments fiber breakage was seen to be present, especially for long fiber groups, although in an over-all sense it was fairly small. Fiber breakages into more than four segments were negligible. These will, of course, depend on the particular breakage process under study. It is demonstrated that the model can be used to assess analytically whatever the mode of ordinary random fiber breakages, allowing more flexible relation between breakage probability and fiber length and taking multi-segments fiber breakage into account.