信頼性工学 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 （第３報） 極値統計解析による最大き裂長さの推定精度 理論解析とシミュレーションの推定精度が異なる要因

Abstract

In recent years, attempts have been made to apply the statistics of extremes to the estimation of maximum crack length in a structural component. However, a guide for determining the sample area S and the number of divisions m that influence the estimation accuracy of maximum crack length have not been obtained. In a previous paper, the authors showed that √V(Xmax)/σ by the theoretical analysis is not equal to √V(Xmax)/σ by Monte Carlo simulation for the case when crack lengths follow exponential and Weibull distributions, where √V(Xmax) is the root mean squared error of the estimated value, and σ is the variance of the double exponential distribution which the largest crack length in each elemental area follows. It was also shown that this difference was due to √V(Xmax). In the present paper, it is shown that the difference in values is due to the fact that the theoretical analysis differs from Monte Carlo simulation in the definition of the true maximum crack length, Xmax, for the case when crack lengths follow an exponential distribution. It is also shown that the difference in values is due to the fact that the theoretical analysis differs from Monte Carlo simulation in the definition of Xmax and that the largest crack length in each elemental area by Monte Carlo simulation does not strictly follow the double exponential distribution for the case when crack lengths follow a Weibull distribution.