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.