The risks associated with extrapolations are quantified by simulation for the case of metal fatigue data. Extrapolations to 1% failures are made from samples of 10 or 20 or 50 specimens for four assumed distributions of the failures. Two methods of extrapolation are investigated. Method A corresponds to straight line fitting on lognormal probability paper. Method B applies extreme value theory to the 40% smallest values in a sample and gives superior results for samples of 50 specimens. For the small samples usual in metal fatigue, Method A gives equally good (or poor) results. Results are presented in several measures. An empirical risk divisor is introduced as a practical means of reducing the risk.
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