Abstract: Whether from the perspective of engineering application of establishing N\text - v_\texts relationship curve in a region or as an essential part of regional soil characteristic theory, the number of arrays required for constructing scientific N\text - v_\texts function is an important problem, but this issue has not been involved before. The stability and convergence of N\text - v_\texts characteristic functions under different sample numbers are studied by using the random analysis of measured data, and the array thresholds for constructing N\text - v_\texts characteristic functions with different precisions are proposed. The measured data come from 9 regions in four countries, and there are 11 working conditions in total. The results of random analysis show that the N\text - v_\texts characteristic function is stable and convergent with the increase of the number of samples. The research shows that if the N\text - v_\texts array exceeds 50, 100, 200 and 800 in a region, the N\text - v_\texts characteristic functions with coefficients of variation less than 0.2, 0.15, 0.10 and 0.05 can be obtained respectively.