A Probability Model for Random Fiber Breakages

Abstract

For a given fiber group of any particular length from a given fiber population, two fundamental questions in connection with random breakages of fibers are set forth about the probability of a fiber breaking at all and the probability of a fiber breaking into s segments (s ≥ 2). In order to elucidate such questions, a probabilistic model for the random fiber breakage is derived, allowing multi-segment fiber breakage and more flexible relation (linear or non-linear) between fiber breakage probability and fiber length. Fiber weight distribution is defined, and a model is established so that available sample fiber-weight distributions, in the form of discrete densities, determined, by existing fiber testing technique in practice can be directly used. An axiomatic inter pretation of the breakage process naturally results from the model in a matrix expression.