There are many tests for statistical distribution, such as KS test, chi square test, etc. from the perspective of graphics, QQ chart or PP chart can also be used to check whether the data obey a certain distribution. As shown in Fig. 1 ~ Fig. 4, the P-P scatter diagram is used to verify the fitting superiority of common distribution and empirical distribution. If the data points are near the empirical distribution line y x =, it is considered that the distribution type fits well.
According to the P-P scatter diagram corresponding to the defect size, the data points of lognormal distribution are the closest, indicating that the exponential distribution and lognormal distribution fit well with the empirical distribution. The fitting effect can also be seen intuitively from Fig. 5 and Fig. 6, while the normal distribution can not accurately describe the distribution of defect size.
Figure 5 and Figure 6 show the relationship between the length of a defect and its occurrence probability. The larger the length of the defect, the smaller the probability of occurrence, and the smaller the length of the defect, the greater the probability of occurrence. If the influence of small defects less than 10mm on cast steel joints is not considered, it can be predicted that defects with a length of 10mm ~ 20mm will account for 95.49% of the total defects, and defects with a length of 20mm ~ 30mm will account for 4.30%.
