A statistical analysis of hair breakage. II. Repeated grooming experiments

The objective of this work was to introduce the idea of analyzing data from repeated brushing and combing experiments on hair in accordance with standard fatigue testing approaches. In mechanical testing terms, the brushing and combing of hair represents a fatiguing process wherein individual strands experience repeated exposure to an external stimulus. Therefore, in accordance with fatiguing principles, one expects a gradual propagation of flaws within individual fibers until, ultimately, catastrophic failure (breakage) results. A previous paper in this series described the modeling of single-fiber fatigue data using the Weibull approach, and, in so doing, introduced the idea of treating fiber breakage as a statistical variable. Here, a grouped Weibull methodology was used to analyze breakage data from repeated brushing and combing experiments. At a top level, the generation of the two Weibull parameters provides a means of characterizing these experiments. However, the real strength of the approach involves the ability to generate survival probability plots that provide predictions as to the likelihood of fiber breakage under different conditions. Therefore, assuming laboratory experiments are a reasonable representation of real-life conditions, it becomes possible to predict breakage rates on actual heads as a function of different habits and practices. It is also shown how the two Weibull parameters, together with information about the number of fibers in the test tresses, allow for the modeling of repeated brushing and combing tests and allow anyone to re-create the experimental outcome for comparison to their own experiences. These principles have been demonstrated using experiments that compare breakage in virgin and chemically damaged hair, while also showing how conditioning treatments provide considerable retardation.