Suitable sample area and number of divisions in the estimation of the maximum crack length by extreme value analysis: Evaluation of estimation accuracy independent of distribution forms

In estimating the maximum crack length in a structural component by statistics of extremes, one encounters the problem of how to choose the sample area S (the ratio of the sample area to the whole area) and the number of divisions m. In a previous paper, the present authors showed that the root-mean-square error of the estimated value, √V(X max ) can be approximated by a linear function of log S for the case where individual crack lengths follow an exponential distribution. In the present paper, by conducting a theoretical analysis and Monte Carlo simulation, it is shown that √V(X max )/σ can be approximated by a linear function of log T regardless of the distribution forms of individual crack lengths, where a is the standard deviation of the double exponential distribution which the largest crack length in each elemental area follows, and T(= m/S) is the return period. It is also shown that √V(X max )/σ by Monte Carlo simulation is 1.1 to 1.9 times larger than that calculated by theoretical analysis. Causes for this difference are discussed.