Estimation accuracy of maximum crack length by extreme value analysis
- Factor of difference in estimation accuracy between theoretical analysis and Monte Carlo simulation-
Matsumura Takashi; Ichikawa Masahiro
Abstract:In recent years, attempts have been made to apply the statistic 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 square root of V(X^max)/s by the theoretical analysis is not equal to square root of V(X^max)/s by Monte Carlo simulation for the case when crack length follow exponential and Weibull distribution, 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, It was also shown that this difference was due to square root of V(X^max). 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 length follows 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 dose not strictly follow the double exponential distribution for the case when crack lengths follow a Weibull distribution. Key Words:reliability, maximum crack length, remaining life, extreme value analysis, Monte Carlo simulation