Submitted:
19 March 2025
Posted:
19 March 2025
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Abstract
Keywords:
1. Introduction–Collected Data
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2. Results and Discussion
2.1. Comparison of the Average Monthly Capacities of the Tested Conveyors


2.2. Statistical Analysis of Conveyor Capacities
| Descriptive Statistics | Conveyor A | Conveyor B | Absolute Difference | Relative Difference (%) |
|---|---|---|---|---|
| No. of Measurements | 36 | 48 | 12 | 33.33 |
| Mean in Mg/h | 2,370.56 | 2,296.89 | -73.67 | -3.11 |
| Median in Mg/h | 2390.60 | 2,286.37 | -104.23 | -4.36 |
| Geometric Mean in Mg/h | 2,366.14 | 2,292.63 | -73.51 | -3.11 |
| Harmonic Mean in Mg/h | 2,361.69 | 2,288.42 | -73.27 | -3.10 |
| Standard Deviation in Mg/h | 146.62 | 142.20 | -4.42 | -3.02 |
| Coefficient of Variation | 6.19% | 6.19% | 0.10 | 0.10 |
| Standard Error in Mg/h | 24.437 | 20.525 | -3.912 | -16.01 |
| Variance in Mg2/h2 | 21,498.1 | 20,221.2 | -1276.9 | -5.94 |
| Minimum Capacity in Mg/h | 2119.17 | 2045.89 | -73.28 | -3.46 |
| Maximum Capacity in Mg/h | 2693.29 | 2692.01 | -1.28 | -0.05 |
| Range in Mg/h | 574.12 | 646.12 | 72.00 | 12.54 |
| Lower Quartile (Q1) in Mg/h | 2307.98 | 2200.30 | -107.68 | -4.67 |
| Upper Quartile (Q3) in Mg/h | 2445.07 | 2409.83 | -35.24 | -1.44 |
| Interquartile Range in Mg/h | 137.10 | 209.53 | 72.44 | 52.84 |
| Skewness | 0.0178 | 0.4232 | 0.4053 | 2273.16 |
| Kurtosis | -0.0170 | 0.0559 | 0.0729 | -427.76 |
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Consistent Variation:
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- The coefficient of variation was nearly identical (6.19%) for both conveyors despite differences in mean values.
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- The maximum capacities were almost the same (~2,693 Mg/h), while the minimum capacity was lower for Conveyor B.
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Higher Dispersion in Conveyor B:
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- The range of fluctuations in Conveyor B’s capacity was 72 Mg/h higher than in Conveyor A (646.12 Mg/h vs. 574.12 Mg/h).
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- This wider range may be due to seasonal and operational factors, requiring further investigation.
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Efficiency Distribution Differences:
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- Interquartile and intersextile ranges suggest a more concentrated distribution in Conveyor A, while Conveyor B exhibited greater dispersion at the extremes.
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- The kurtosis values suggest that both datasets approximate a normal distribution, though Conveyor A’s slight negative kurtosis (-0.017) contrasts with Conveyor B’s positive kurtosis (0.056).
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- Conveyor B exhibited stronger right-side skewness (0.42), indicating higher occurrences of lower-than-average capacities than Conveyor A (skewness = 0.017).
2.1.1. Statistical Significance of Differences in Monthly Average Capacities
- Confidence Intervals for Monthly Average Capacities
- Conveyor A: 2,370.56 ± 49.61 [2,320.95; 2420.17]
- Conveyor B: 2,296.89 ± 41.29 [2,255.59; 2338.18]
- ZE Difference: 73.67 ± 63.21 [10.47; 136.88]
- Student’s t-Test for Mean Comparison
- t-statistic: 2.31884
- P-value: 0.02289
- F-Test for Variance Comparison
- Conveyor A: 146.622 [118.92; 191.26]
- Conveyor B: 142.201 [118.38; 178.18]
- Variance Ratio: 1.0632
- 95% Confidence Interval for Variance Ratio: [0.57575; 2.0211]
- Mann-Whitney (Wilcoxon) Test for Median Comparison
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Median Capacities:
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- Conveyor A: 2,390.6
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- Conveyor B: 2,286.37
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Mean Ranks:
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- Conveyor A: 49.6111
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- Conveyor B: 37.1667
- W-statistic: 608
- P-value: 0.02092
- Kolmogorov-Smirnov Test for Distribution Compatibility
- DN Statistic: 0.3819
- K-S Statistic: 1.7323
- P-value: 0.00049


2.3. Regression of the Unit Energy Consumption Indicator ZE Against the Average Capacity of the Conveyor


- Correlation coefficient: 0.854862
- R-squared: 73.0789%
- R-squared (df corrected): 72.2871%
- Standard error of estimation: 0.0000796077
- Mean absolute error: 0.0000882741
- Durbin-Watson statistic: 0.909369 (P = 0.00001)
- Residual autocorrelation Lag 1: 0.335697
| Least squares method | Standard | Statistics | Value | ||
|---|---|---|---|---|---|
| Parameter | Estimate | Error | T | P | |
| Offset | 0.0005512 | 0.00030525 | 1.8057 | 0.0798 | |
| Slope | 0.000001235 | 1.2853 E-7 | 9.6070 | 0.0000 | |
| Variance Analysis | |||||
| Source | Sum of squares | Df | Medium squares | F-statyst. | Value P |
| Model | 0.0000011472 | 1 | 0.0000011472 | 92.30 | 0.0000 |
| The Rest | 4.22607 E-7 | 34 | 1.24296 E-8 | ||
| Together (Corr.) | 0.00000157 | 35 | |||

- Correlation coefficient: 0.86031
- R-squared: 74.012%
- Standard error of estimation: 0.00010734
- Mean absolute error: 0.000089
- Durbin-Watson statistic: 0.58731 (P = 0.0000)
- Residual autocorrelation Lag 1: 0.66312
| Least squares method | Standard | Statistics | Value | ||
|---|---|---|---|---|---|
| Parameter | Estimate | Error | T | P | |
| Offset | 0.00041227 | 0.00025337 | 1.6277 | 0.1105 | |
| Slope | 0.0000012602 | 1.10102 E-7 | 11.446 | 0.0000 | |
| Variance Analysis | |||||
| Source | Sum of squares | Df | Medium squares | F-statyst. | Value P |
| Model | 0.0000015094 | 1 | 0.0000015094 | 131.01 | 0.0000 |
| The Rest | 5.29975 E-7 | 46 | 1.15212 E-8 | ||
| Together (Corr.) | 0.000002039 | 47 | |||

- Correlation coefficient: 0.86312
- R-squared: 74.498%
- Standard error of estimation: 0.00011448
- Mean absolute error: 0.000088274
- Durbin-Watson statistic: 1.0102 (P = 0.0000)
- Residual autocorrelation Lag 1: 0.46853




3. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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| Conveyor construction data | A | B |
|---|---|---|
| Length in m | 1012.6 | 1018.5 |
| Belt speed in m/s | 5.24 | 5.24 |
| Theoretical mass capacity in Mg/h | 6400 | 6400 |
| Theoretical volume capacity Mg/h | 8000 | 8000 |
| Number of pulleys in a set | 3 | 3 |
| Idler length in mm | 670 | 670 |
| Idler diameter in mm | 191 | 191 |
| Idler set spacing in m | 1.24 | 1.24 |
| Trough angle | 45 | 45 |
| Belt type | St3150 | St3150 |
| Belt width in mm | 1800 | 1800 |
| Coal bulk density in Mg/m3 | 0.8 | 0.8 |
| Collected operating data | A | B |
|---|---|---|
| Number of monthly measurements | 36* | 48 |
| Total mass transferred in Mg | 42 096 610 | 46 540 032 |
| Total operating time in hours | 17 672.9 | 20 151.84 |
| Total energy consumption in MWh | 12 058.42 | 13 994.02 |
| Average monthly operating time in hours | 490.91 | 419.83 |
| Standard deviation | 60.98 | 91.28 |
| Coefficient of variation in % | 12.42% | 21.74% |
| Minimum | 352.1 | 198.6 |
| Maximum | 629.4 | 584.7 |
| Range of change | 277.3 | 386.1 |
| The average amount of mass transferred in Mg | 1 169 350 | 969 584 |
| Standard deviation | 198 752 | 243 846 |
| Coefficient of variation | 17.00% | 25.15% |
| Minimum | 760 503 | 424 723 |
| Maximum | 1 695 160 | 1 574 020 |
| Range of change | 934 657 | 1 149 297 |
| Average energy consumption in MWh | 334.956 | 291.542 |
| Standard deviation | 43.88 | 62.97 |
| Coefficient of variation | 13.10% | 21.60% |
| Minimum | 212.0 | 140.7 |
| Maximum | 441.6 | 406.5 |
| Range of change | 229.6 | 265.8 |
| Calculated capacities and ZE indicators | A | B |
|---|---|---|
| Average efficiency for total values in Mg/h | 2 381.99 | 2 309.47 |
| The degree to which the theoretical capacity was utilized in % | 37.22% | 36.09% |
| Unit indicator ZE for total energy consumption in Wh/Mg/km | 286.45 | 300.69 |
| Average monthly efficiency Q in Mg/h | 2 370.56 | 2 296.89 |
| Standard deviation | 146.622 | 142.201 |
| Coefficient of variation | 6.19% | 6.19% |
| Minimum | 2 119.17 | 2 045.89 |
| Maximum | 2 693.29 | 2 692.01 |
| Range of change | 574.12 | 646.12 |
| ZE indicator in Wh/Mg/km | 288.57 | 303.58 |
| Standard deviation | 18.18 | 19.12 |
| Coefficient of variation | 6.30% | 6.30% |
| Minimum | 256.87 | 254.7 |
| Maximum | 336.35 | 344.57 |
| Range of change | 79.48 | 89.87 |
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