## 4 Experimental Results
### Measurement Statistical Analysis Experimental of Varying Orientations of the Measurement Object
(**a**) \(750.0\times 495.0\times 330.0\); (**b**) \(480.0\times 550.0\times 380.0\); (**c**) \(450.0\times 650.0\times 350.0\). In this experiment, we evaluated the stability of the measurement system by making repetitive measurements of the box dimension. We used four standard boxes for measurement experimental to increase the credibility of the experiment. As shown in Figure 16a-d, the side length of the box is evenly distributed within the measurement interval of the measuring range, and L, W, and H of these standard boxes are \(110.6\times 410.5\times 620.8\), \(390.8\times 240.6\times 530.7\), \(1110.7\times 750.8\times 880.9\), and \(690.7\times 570.5\times 1500.0\), respectively. The position of the box relative to the vision sensor in each shot was changed, so the measured value can be used to verify the measurement accuracy of the system. The experimental results (L, W, and H) of measurements for the standard boxes are shown in Table 6. The average estimated values were recorded as the average of 15 experimental sessions on the standard box with the best distance from the box-sensors. The stability analysis and the evaluation of uncertainty in the measurement experimental of the measurement system were evaluated by performs data statistics on the results of 15 measurements, and the mean (Mean), average absolute error (Ave_Err), standard deviation (Std), and the uncertainty of class A (\(\mu_{\text{A}}\)) were calculated. The formula for calculating \(\mu_{\text{A}}\) is as follows:  
\[\mu_{\text{A}}=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(x_{i}-\overline{x} \right)^{2}}{n-1}} \tag{16}\]  
where x\({}_{i}\) is the measured data and \(\overline{x}\) is the mean of the measured data. n is the number of measurements, which is 15 in the experiment. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & **W** & **L** & **H** & **W** & **L** & **H** & **W** & **L** & **H** & **W** & **L** & **H** \\  & **(a)** & **(a)** & **(a)** & **(b)** & **(b)** & **(b)** & **(c)** & **(c)** & **(c)** & **(d)** & **(d)** & **(d)** \\ \hline
1 & 110.5 & 410.1 & 620.3 & 3 The standard deviation of the measurement results was analyzed in accordance with the actual length of the measured boxes. The maximum value of standard deviations was less than 2.68 mm, and the minimum value of the standard deviation was less than 1.01 mm, indicating that the box measurement system has reliable repeated measurement accuracy. Ave_Err and \(\mu_{\text{A}}\) in the computed dimensions increased as the measurement range of the system increased. This phenomenon is attributed to the relative error that tends to decrease as the distance of the visual sensor and box becomes small. Figure 17a,b show the average error distribution and the measurement uncertainty of the system of these 15 measurements and are consistent with the theoretical analysis. The maximum absolute error of the side length of the standard box is 4.7 mm. The measurement uncertainty of the measuring system is \(\pm\)1.05 mm to \(\pm\)2.77 mm within the range of 110-1500 mm, indicating that the measurement system has high reliability in actual measurement and strong practical application.