HAIR BREAKAGE: REPEATED GROOMING EXPERIMENTS 449 WEIBULL ANALYSIS IN THE MODELING OF REPEATED GROOMING EXPERIMENTS The inverse of a survival probability curve is a failure probability curve. That is, a 99% likelihood of survival equates to a 1% chance of failure. As such, by calculating a failure probability and multiplying results by the number of fi bers in our test tresses (approxi- mately 2,500 in this instance), we obtain a model that is able to describe the whole ex- periment. Figure 8 shows such models, together with actual experimental results, for our virgin hair and conditioned hair experiments. This also illustrates how the reporting of the Weibull parameters (together with the number of fi bers in the tresses) provides an extremely useful means of documentation, as it allows anyone to recreate the whole ex- periment for comparison and contrasting purposes. Figure 7. Survival probability plot for brushing virgin and conditioned Caucasian hair at 60% RH. Figure 8. Models and experimental data for repeated grooming experiments on virgin and conditioned Caucasian hair at 60% RH.

JOURNAL OF COSMETIC SCIENCE 450 By means of illustration, Table III shows Weibull parameters obtained from a series of experiments that were intended to investigate the infl uence of different experimental variables, while Figure 8–11 show the models generated by these values in comparison to the experimental data. Figure 9 shows models, plus experimental data, for virgin and bleached hair, and illus- trates the higher incidence of breakage that occurs as the result of chemical damage. Figure 10 shows the effect of conditioning on bleached hair and illustrates the still-greater benefi t of these treatments on damaged hair. Meanwhile, Figure 11 shows how breakage greatly increases upon repeated chemical treatment of hair. An unexpected fi nding from our single-fi ber fatigue work involved an especially dramatic effect relating to the relative humidity of the environment. While it is well recognized that the mechanical properties of hair change as a result of the relative humidity dictating the moisture content of hair, it was found that a massively larger infl uence was obtained on fatigue testing results as compared to conventional stress-strain experiments. Figure 12 shows models and experimental data resulting from repeated grooming of virgin Cau- casian hair as a function of the relative humidity. Findings from these experiments are in line with predictions from the single-fi ber work. Figure 9. Models and experimental data for repeated grooming experiments on virgin and bleached Cauca- sian hair at 60% RH. Table III Weibull Parameters for Repeated Brushing Experiments on Caucasian Hair after Different Treatments Treatment Characteristic lifetime Shape factor Virgin hair 55,200,000 0.48 Conditioned hair 1,040,000,000 0.43 1× Bleached hair 3,480,000 0.64 Conditioned bleached hair 1,510,000,000 0.54 3× Bleached hair 538,000 0.61