極値統計解析による最大き裂長さの推定における抽出面積と分割数 : き裂長さの原分布形をワイブル分布と仮定した場合の推定精度の評価

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In order to assure the maintainability and reliability of structural components, it is important to examine the structural components for damage and to estimate their remaining life. In recent years, attempts to apply statistics of extremes to the estimation of maximum crack length in a structural component have been made. In such estimation, it is necessary and important that the sample area is made as small as possible to restrain the labor for taking small cracks and measuring crack lengths and that the estimate of maximum crack length satisfies the needed accuracy of estimation. However, a guide for determining the sample area S(the ratio of the sample area to the whole area)and the number of division m that satisfy these two conditions has not been obtained. In the present paper, as a part of the study to obtain this guide, the relationship of √<V(X^^^_<max>)>/σ to log T is examined by conducting Monte Carlo simulation for the case when crack length follow a Weibull distribution(shape parameter α=0.8, 2.0), where √<V(X^^^_<max>)>/σ is the root mean squared error of the estimated value, σ is the variance of the double exponential distribution which the largest crack length in each elemental area follows, and T(=m/S)is the return period. As a result, it is shown that √<V(X^^^_<max>)>/σ by Monte Carlo simulation is not equal to √<V(X^^^_<max>)>/σ(the result of a previous paper)by the theoreti calanalysis quantitatively and that the cause for this difference is not σ but √<V(X^^^_<max>)>/σ. It is also shown that √<V(X^^^_<max>)>/σ by Monte Carlo simulation for the case when individual crack length follows a weibull distribution is not equal to √<V(X^^^_<max>)>/σ (the result of a previous paper)by Monte Carlo simulation for the case when individual crack lengths follow an exponential distribution quantitatively.
社団法人日本材料学会の論文
1998-03-15

極値統計解析による最大き裂長さの推定における抽出面積と分割数 : き裂長さの原分布形をワイブル分布と仮定した場合の推定精度の評価

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