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 : 分布形によらない推定精度の評価(<特集>信頼性工学)

概要

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In the estimation of maximum crack length in a structural component by the 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 division m. In a previous paper, the present authors showed that the root mean squared error of the estimated value, √<V(X^^^_<max>)> can be approximated by a linear function of log S for the case when individual crack lengths follow an exponential distribution. In the present paper, by conducting 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 variance 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 1.1〜1.9 times larger than that by the theoretical analysis. The causes for this difference are discussed.
社団法人日本材料学会の論文
1995-05-15