Use of simulation modelling for checking monitoring and testing procedures

Analysis of Requirements and the Feasible Limit for Error Reduction in Two-Parameter Magnetic Determination of Steels’ Hardness

“…The value σ F shows how the use of the second parameter x 2 to determine the value of F decreases (if σ F < 1) or increases (if σ F > 1) the SD of the indirect measurement according to equation (3) compared to using only the parameter x 1 . In the notation (7), from (6) we obtain: Figure 1 shows the results of calculating the dependences σ F = σ F (σ 2 ) by formula (8) in the range 0 ≤ σ 2 ≤ 3 for different coefficients R of the correlation between the parameters x 1 and x 2 in the possible range -1 ≤ R ≤ 1 of its change. Figure 2 shows the results of calculating the dependences by σ F = σ F (R) formula (8) at different values in the range of -1 ≤ R ≤ 1.…”

“…In the notation (7), from (6) we obtain: Figure 1 shows the results of calculating the dependences σ F = σ F (σ 2 ) by formula (8) in the range 0 ≤ σ 2 ≤ 3 for different coefficients R of the correlation between the parameters x 1 and x 2 in the possible range -1 ≤ R ≤ 1 of its change. Figure 2 shows the results of calculating the dependences by σ F = σ F (R) formula (8) at different values in the range of -1 ≤ R ≤ 1. Taking into account the symmetric influence of the parameters x 1 and x 2 on the result of calculating the value of F (x 1 , x 2 ) by formula (3), for analysis in the case of 0 ≤ σ 2 ≤ 1, the parameters x 1 and x 2 can be swapped and the case σ 2 ≥ 1 can be considered.…”

“…At 1 ≤ σ 2 < 3, the value decreases as R decreases and approaches the value -1. From (8) it follows that the condition σ F ≤ y is satisfied for values of R satisfying the equation: Figure 1 -Dependence of the relative standard deviation σ F of the results of determining the physical quantity F according to the formula (3) on the relative standard deviation σ 2 of the second parameter: 1 -7 -respectively at R = 1; 0.5; 0; -0.5; -0.8; -0.9; -1. Calculation according to the formula (8) Figure 3 shows the isolines of the function σ F = y at different y in coordinates (σ 2 , R).…”

“…To increase the reliability of magnetic structural analysis, a combined use of several magnetic parameters was proposed. Analysis of the theoretical foundations of such methods, experiments, and modeling showed a strong influence of errors in measuring the parameters used in multiparameter regression equations on the reliability of control [6][7][8][9][10]. Nevertheless, multi-parameter models are used to calculate the hardness of HRC steels [11,12].…”