In reality, values of a specimen (its strength, etc.) have certain probability distributions. Deterministic values in reality are also uncertain and have error margins. Thus, averages and standard deviations are used for estimates in engineering and nature, and major factors in estimations are based on the nominal value and the upper and lower allowed (survival, design, standards) limits. Observations beyond those limits indicate mostly a failure. However, probability distributions in nature and engineering show a relatively long “tail” beyond the limits of several standard deviations. The values of deviations from the mean (or target) can be very large, which can endanger the whole specimen. The phenomena at the “tail” domain (and not in the domain up to the limits) are the main reason for the fact that larger specimens are generally more vulnerable than smaller ones, having the same mean and probability distribution. The present paper extends this concept to relevant phenomena in nature and in technology.
distribution tails, probability distributions, size effect, statistics, strength of specimen, upper standard limit
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