Suitable sample area and number of division in estimation of maximum crack length by extreme value analysis
- Evaluation of estimation accuracy for the case when crack lengths follow a Weibull distribution -
Matsumura Takashi; Ichikawa Masahiro
Abstract:In order to assure the maintainably 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 the statistic 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 divisions 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 square root of V(X^max)/s to logT is examined by conducting Monte Carlo simulation for the case when crack length follow a Weibull distribution (shape parameter a = 0.8, 2.0), where square root of V(X^max) is the root mean squared error of the estimated value, and s is the variance of the double exponential distribution which the largest crack length in each elemental area follows, and T =(m/S) is return period. As a result, it is shown that square root of V(X^max)/s by Monte Carlo simulation is not equal to square root of V(X^max)/s (the result of a previous paper) by the theoretical analysis quantitatively and that the cause for this difference is not s but square root of V(X^max)/s. It is also shown that square root of V(X^max)/s by Monte Carlo simulation for the case when individual crack length follows a Weibull distribution is not equal to square root of V(X^max)/s (the results of a previous paper) by Monte Carlo simulation for the case when individual crack length follow an exponential distribution quantitatively. Key Words:reliability, maximum crack length, remaining life, extreme value analysis, Monte Carlo simulation