Simulation of the estimation of the maximum inclusion size from 2-dimensional observation data on the basis of the extreme value of statistics

It is well known that the large-scale inclusions in steel act as the destruction starting point of the material. The labor is extremely necessary for investigating the maximum inclusions that have been distributed in the matrix of a large volume. The statistics of extreme value method is an excellent technique that can be applied for that case. When a material such as steel is opaque to visible light, the electron beam, and so on, the evaluation of the internal inclusions as three-dimensional (3D) information is presumed from the two-dimensional (2D) information observed under a microscope in respect of sample cross section. It is expected that this presumption error margin is large. It is almost impossible to verify 2D data by 3D one in a real material because the true value is uncertain, especially concerning the information of the tail of the size distribution. The purpose of the present work is to offer statistical information necessary to presume 3D characteristic value from 2D measurement data with respect to the maximum extreme value. The simulation whose 3D characteristic value is already-known is effective to this. Some 3D size distributions such as the exponential, log-normal, pseudo-normal, and Rayleigh distribution is set here, and how the 2D maximum extreme-value distribution (MED) changes into the measured number of sections is shown. The result gives a number of sections necessary to gather data with few error margins directly. Further, some findings of the relation between 3D-MED and 2D-MED are given. The overarching point is a type of the MED and conversion of the dimension.