Hair Breakage 270 Table 4. Illustration of how single fiber fatigue data is modeled by Weibull analysis (Caucasian hair under a 0.010-0.011 g/um2 stress at 60% RH) Cycles-to-fail Rank Median Rank 1/(1-Median Rank) l n(ln(1/(1-Median Rank) ln(cycles-to- fail) 901 1 0.009284 1.009371 -4.67482 6.803505 1361 2 0.022546 1.023066 -3.7808 7.215975 1574 3 0.035809 1.037139 -3.31138 7.361375 2089 4 0.049072 1.051604 -2.98942 7.644441 3434 5 0.062334 1.066478 -2.74324 8.141481 300,000 73 0.964191 27.92593 1.202839 12.61154 300,000 74 0.977454 44.35294 1.332941 12.61154 300,000 75 0.990716 107.7143 1.543187 12.61154 Table 5 shows characteristic lifetimes and shape factors as a function of stress for virgin Caucasian hair tested at 60% RH. The results for each stress range represent an analysis of 75 individual fibers. Characteristic lifetimes again reflect the exponential relationship between the cycles-to-fail and the applied stress. Meanwhile, shape parameters approximating unity suggest results for each data-set generally abide by an exponential distribution function. Table 5. Weibull parameters for Caucasian hair at 60% RH as a function of applied stress Stress Range Characteristic lifetime, α Shape factor, β 0.014‑0.015 g/μm2 1,260 1.07 0.013‑0.014 g/μm2 1,970 1.06 0.012‑0.013 g/μm2 6,030 0.89 0.011‑0.012 g/μm2 18,100 0.79 0.010‑0.011 g/μm2 35,800 0.86 0.009‑0.010 g/μm2 158,000 0.80