Statistical Treatment of Data and Extreme-Value Theory in Relation to Fatigue in Textiles

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Abstract
The use of central measures of lifetime to characterize fatigue behavior is misleading, and more attention should be paid to early failures and expected minimum life. Differences in the dispersions of lifetimes between samples may lead to faulty conclusions if these are based on mean lifetimes. The possible dependence of dispersion on stroke is considered. Because of dispersion in fatigue data, it is necessary to test large numbers of specimens to make reliable predictions. The inadequacy of observed central values as bases for judging the applicability of a distribution is discussed. Criticism leveled against the commonly used logarithmic-normal distribution is cited. Criteria are presented for the development of a lifetime distribution that takes into account the physical realities of the fatigue process. Analytical expressions for a number of concepts in the statistics of fatigue are reviewed. The theory suggesting the application of the third asymptotic distribution is outlined. The distribution has been adapted to accumulated fatigue data on an acrylic fiber sample.

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