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Since the chain-type weak-link theory was first proposed by Pierce in 1926, many items in the literature have referred to it in one form or another. There has, however, been little extensive testing of this theory for either yarns or individual fibers. In this paper, the hazard function is used as a sensitive test for the data of Pierce on cotton yarns, those of Moreton on carbon filaments, and data gathered in the authors' laboratory on viscose rayon filaments. In each of these cases, it is shown that the theory does not apply. Alternate models are proposed and the most tractable of these is discussed in detail. Parameters in this model are estimated for the viscose rayon data. [ABSTRACT FROM PUBLISHER]