PRACTICAL MODERN HAIR SCIENCE (FREE COPY) Page 290 (290 of 545)

Chapter 8 283 Table 10. Grouped Weibull analysis of repeated brushing data for virgin Caucasian hair at 60% RH *Note on the value on N in the Median Rank calculation: The average number hair fibers in the tresses used in this work is approximately 2,500 fibers therefore the total number of fibers across eight tresses (i.e. N in the median rank equation) is 20,000. Grooming Cycles # 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 22. Mean values for the number of broken fibers after brushing virgin hair tresses 10,000 times

Previous Page Next Page

PRACTICAL MODERN HAIR SCIENCE (FREE COPY) resources

Attachments

Follow Link PMHS_with title page_OCR.pdf

Extracted Text (may have errors)

Chapter 8 283 Table 10. Grouped Weibull analysis of repeated brushing data for virgin Caucasian hair at 60% RH *Note on the value on N in the Median Rank calculation: The average number hair fibers in the tresses used in this work is approximately 2,500 fibers therefore the total number of fibers across eight tresses (i.e. N in the median rank equation) is 20,000. Grooming Cycles # 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 22. Mean values for the number of broken fibers after brushing virgin hair tresses 10,000 times

Help

Hair Breakage 282 The device consists of a hollow rotating drumlike assembly, where four outer crossbars contain holders for mounting combs or brushes. These outer arms are detachable and allow for use of different combs or brushes. The brushes/combs are mounted at 90-degree angles, allowing one complete drum revolution to brush (or comb) a tress four times. This entire arrangement is duplicated three times in the horizontal direction allowing four tresses to be combed simultaneously. Collection plates are located under each tress to save broken fiber fragments, while spacer plates on the rotating drum prevent cross-contamination. By adopting learning from the single fiber fatigue work, it becomes possible to recognize how a number of variables can influence the outcome of these experiments. For example, a combination of the size and shape of hair tresses, the tooth-spacing of the brush or comb, and the condition of the hair will all dictate the magnitude of the grooming stresses and consequently influence the amount of breakage. In addition, the need for performing experiments under controlled humidity conditions is apparent. A more comprehensive discussion involving the contribution of these variables has been given previously.12 Results: Figure 22 shows a Box & Whisker plot for the number of broken fibers arising from repeated grooming of virgin Caucasian hair treated with a commercially available conditioner product relative to an unconditioned state. Results convincingly illustrate the benefit provided by such products, in that the extent of breakage in this particular instance has been reduced by approximately 60%. However, with some slight modification to the method, it becomes possible to perform Weibull analyses and model the tendency for breakage throughout the experiment. Grouped Weibull analysis: Table 10 shows how repeated grooming experiments can be setup in a manner that allows for performing a grouped Weibull analysis.6 It is seen that the number of broken fibers is evaluated at regular intervals throughout the experiment. Column 2 shows the total number of broken fibers (from eight replicate hair tresses) after grooming in 1,000 cycle

Previous Page Next Page

PRACTICAL MODERN HAIR SCIENCE (FREE COPY) resources

Hair Breakage 284 blocks. Column 3 then shows a running total of the number of broken fibers (i.e. a cumulative breakage frequency) from which a Weibull analysis can be performed. Therefore, Column 4 again shows the median rank approach for estimating the cumulative distribution function, while Columns 5 and 6 show the creation of the double log expression that forms the y axis in the Weibull plot and Column 7 represents the x axis. As before, it is convenient to set- up all calculations in an Excel spreadsheet. Figure 23 shows the Weibull plot that is obtained from the data in Table 10, and the subsequent evaluation of the two Weibull parameters. Therefore, under these conditions, we obtain a characteristic lifetime (α) of 55.2 million grooming strokes and a shape parameter (β) of 0.48. As described earlier, a shape parameter less than one is indicative of a process where the highest rate of breakage occurs early in the experiment (see Column 2 in Table 10) and represents a premature failure mechanism. Of course, there is danger in ascribing too much significance to the long range extrapolation that yields the magnitude of the characteristic lifetime. That is, a prediction that 55.2 million grooming strokes would be required in order to break 63.2% of the hair fibers, based on an experiment involving a few thousand cycles, is obviously dubious. Instead, it is emphasized that these two Weibull parameters describe the data over the range of the experiment, and can subsequently be used to generate a Survival Probability plot that again models the test (Figure 24). From this plot it can be predicted that, under these conditions, approximately 1,000 grooming strokes will produce a 0.5% likelihood of fiber breakage, while around 3,500 strokes will yield a 1% likelihood of breakage. These breakage probabilities sound low, at least until projecting results onto actual heads, where it is generally accepted that around 100,000–150,000 fibers are typically present. Therefore, under these conditions, on actual heads, 1,000 grooming strokes would be expected to produce 500–750 broken fibers while 3,500 strokes would yield 1,000–1,500. These numbers no longer sound so trivial, which is one reason why it is prudent to use conditioning products.

Previous Page Next Page

Page 2PMHS_OCR click to expand contents

PRACTICAL MODERN HAIR SCIENCE (FREE COPY) resources

Attachments

Extracted Text (may have errors)

Help

loading

PRACTICAL MODERN HAIR SCIENCE (FREE COPY) resources

PRACTICAL MODERN HAIR SCIENCE (FREE COPY) resources