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

概要

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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 σ 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.
社団法人日本材料学会の論文
1999-03-15