HAIR BREAKAGE: REPEATED GROOMING EXPERIMENTS 447 In this instance, we obtain a characteristic lifetime (α) of 55.2 million grooming strokes and a shape parameter (β) of 0.48. That is, one may predict that 55.2 million grooming strokes would be required in order to break 63.2% of the fi bers. Meanwhile, a shape parameter less than 1 is indicative of a process wherein the highest rate of breakage occurs early in the experiment. Of course, there is danger in ascribing too much signifi cance to the long-range extrapolation that yields the magnitude of the characteristic lifetime. Specifi cally, a prediction involving the outcome after tens of millions of cycles, based on an experiment involving a few thousand cycles, is obviously dubious. Instead, it is em- phasized that together these two Weibull parameters describe the collected data, and, as outlined earlier, can be used to generate a survival probability plot that predicts the Table II Grouped Weibull Analysis of Repeated Brushing Data for Virgin Caucasian Hair at 60% RH Grooming cycles No. of failures Cumulative frequency Median rank 1/(1-Median rank) ln(ln(1/(1-Median rank) Ln (grooming cycles) 1000 110 110 0.00439 1.004407 -5.4267 6.907755 2000 38 148 0.00591 1.005943 -5.1285 7.600902 3000 26 174 0.00695 1.006996 -4.96583 8.006368 4000 19 193 0.00771 1.007768 -4.86165 8.29405 5000 28 221 0.00883 1.008906 -4.72541 8.517193 6000 25 246 0.00983 1.009925 -4.6176 8.699515 7000 25 271 0.0108 1.010946 -4.5202 8.853665 8000 16 287 0.0115 1.011601 -4.46245 8.987197 9000 24 311 0.0124 1.012584 -4.38157 9.10498 10000 15 326 0.0130 1.0132 -4.33412 9.21034 Figure 5. Weibull plot for repeated brushing data of virgin Caucasian hair at 60% RH.

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