# Towards Human–Robot Collaboration in Construction: Understanding Brickwork Production Rate Factors

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## Abstract

**:**

## 1. Introduction

## 2. An Overview of Theoretical Concepts

#### 2.1. Human–Robot Collaboration

#### 2.2. Construction Productivity

#### 2.2.1. Production Rate

#### 2.2.2. Construction Productivity

#### 2.2.3. Factors Affecting Construction Productivity

#### 2.3. Factor Analysis

#### 2.3.1. The Measure of Adequacy/Suitability of Data for Factor Analysis

#### 2.3.2. Principal Component Analysis

#### 2.3.3. Pearson Correlation

#### 2.4. Data Collection

#### 2.5. Measure Adequacy/Suitability of the Dataset for Factor Analysis

#### 2.6. Principal Component Analysis

#### 2.7. Pearson Correlation

## 3. Results

#### 3.1. Descriptive Statistics

#### 3.2. Correlation Method Results

#### 3.3. Suitability for Factor Analysis

#### 3.4. The Result of the PCA Method

#### 3.5. Choice of Principal Components

## 4. Discussion of Results

#### 4.1. Pearson Correlation Results

#### 4.2. Descriptive Statistics

#### 4.3. Adequacy of Data for Factor Analysis and PCA

#### 4.4. Selected Features

## 5. Conclusions and Recommendations

#### 5.1. Conclusions

#### 5.2. Recommendations

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Division/Sub-County | Parishes Chosen | Division/Sub-County | Parishes Chosen | Division/Sub-County | Parishes Chosen |
---|---|---|---|---|---|

Kampala Central | Kamwokya 1 | Kawempe | Kyebando | Nakawa | Banda |

Kisenyi 1 | Bwaise 3 | Mbuya 1 | |||

Kamwokya 2 | Kawempe 3 | Mbuya 2 | |||

Kisenyi 3 | Makerere 2 | Kira Sub-County | Kireka | ||

Rubaga | Kawaala | Makindye | Kisugu | Kyaliwajala | |

Kasubi | Kibuli | Kirinya | |||

Naankulabye | Nsambya Central |

Crew Data | Project Data | Weather Data |
---|---|---|

Mason Number | Wall Length | Sunny/rainy (temperature and precipitation) |

Helper Number | Wall Height | |

Mason Wages | Wall Area | |

Helper Wages | ||

Crew Competency | ||

Work Duration |

Range of Coefficients | Interpretation |
---|---|

[−1,−0.5] ∪ [0.5,1] | a strong negative or positive correlation |

[−0.5,−0.3] ∪ [0.3,0.5] | a moderate negative or positive correlation |

[−0.3,−0.1] ∪ [0.1,0.3] | a weak negative or positive correlation |

[−0.1,0.1] | no correlation |

Variable | Mean | StDev | Variance | Skewness | Kurtosis |
---|---|---|---|---|---|

Mason Size (no) | 2.6 | 0.8 | 0.7 | 0.5 | −0.4 |

Helper Size (no) | 2.4 | 1.1 | 1.2 | 0.3 | −1.1 |

Mason Wages (UGX) | 31,000 | 3839 | 14,736,842 | 0.4 | 0.4 |

Helpers Wages (UGX) | 16,750 | 3354 | 11,250,000 | −0.6 | −0.6 |

Wall Length (m) | 8.1 | 4.49 | 20.2 | 1.0 | 1.1 |

Wall Height (m) | 1.5 | 0.3 | 0.1 | 0.3 | −0.4 |

Wall Built (m^{2}) | 11.6 | 6.3 | 39.9 | 1.0 | 1.1 |

Duration (h) | 7.9 | 0.7 | 0.5 | −4.5 | 20 |

Production Rate (m^{2}/h) | 1.5 | 0.8 | 0.6 | 0.9 | 1.2 |

Variable | Coefficient |
---|---|

Number of Masons | 0.5434 |

Number of Helpers | 0.0234 |

Mason Wages | −0.0238 |

Helper Wages | −0.1254 |

Mason Competency | −0.3464 |

Weather | −0.0607 |

Workday Duration | 0.0628 |

Wall Length | 0.8527 |

Wall Height | 0.7764 |

Wall Built | 0.9978 |

Production Rate | 1.0000 |

Mason Numbers | Helper Numbers | Mason Wages | Helper Wages | Mason Competency | Weather | Man Hours | Wall Length | Wall Height | Wall Area | |
---|---|---|---|---|---|---|---|---|---|---|

Mason Numbers | 1.000 | |||||||||

Helper Numbers | −0.064 | 1.000 | ||||||||

Mason Wages | 0.062 | −0.054 | 1.000 | |||||||

Helper Wages | −0.122 | −0.001 | −0.007 | 1.000 | ||||||

Mason Competency | −0.018 | 0.097 | 0.051 | −0.019 | 1.000 | |||||

Weather | −0.013 | 0.193 | −0.169 | 0.144 | 0.070 | 1.000 | ||||

Man Hours | −0.010 | 0.220 | −0.025 | −0.019 | 0.099 | 0.160 | 1.000 | |||

Wall Length | 0.507 | 0.095 | −0.130 | −0.003 | −0.200 | 0.028 | 0.195 | 1.000 | ||

Wall Height | 0.557 | −0.104 | 0.125 | −0.178 | −0.385 | −0.141 | −0.078 | 0.407 | 1.000 | |

Wall Area | 0.536 | 0.037 | −0.026 | −0.123 | −0.336 | −0.050 | 0.127 | 0.861 | 0.764 | 1.000 |

Kaiser–Meyer–Olkin of Sampling Adequacy | With Wall Area | Without Wall Area | |
---|---|---|---|

0.4739 | 0.5448 | ||

Bartlett Test of Sphericity | Chi-Statistic | 268.2827 | 81.6787 |

Degrees of Freedom | 45 | 36 | |

Significance | 0.000 | 2.11 × 10^{−5} |

Variable | PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 |
---|---|---|---|---|---|---|---|

Number of Masons | −0.392 | 0.478 | 0.443 | −0.134 | −0.176 | 0.144 | −0.499 |

Number of Helpers | 0.201 | 0.176 | 0.106 | 0.922 | −0.033 | −0.094 | −0.066 |

Mason Wages | −0.090 | −0.037 | 0.192 | 0.032 | 0.903 | −0.100 | −0.285 |

Helper Wages | 0.101 | 0.045 | −0.045 | −0.005 | 0.245 | 0.851 | 0.251 |

Mason Competency | 0.386 | −0.115 | 0.828 | −0.155 | −0.067 | −0.082 | 0.317 |

Weather | 0.576 | 0.719 | −0.226 | −0.249 | 0.115 | −0.152 | −0.005 |

Workday Duration | 0.063 | 0.111 | 0.104 | 0.162 | 0.106 | 0.187 | 0.160 |

Wall Length | −0.170 | 0.257 | 0.072 | 0.133 | −0.191 | 0.315 | 0.012 |

Wall Height | −0.524 | 0.359 | 0.019 | 0.035 | 0.164 | −0.269 | 0.689 |

Latent | 0.304 | 0.252 | 0.179 | 0.117 | 0.087 | 0.068 | 0.047 |

Mu | 0.470 | 0.424 | 0.505 | 0.541 | 0.477 | 0.439 | 0.955 |

Explained | 27.072 | 22.47 | 15.954 | 10.464 | 7.789 | 6.029 | 4.180 |

Cumulative Variance | 27.072 | 49.542 | 65.496 | 75.96 | 83.749 | 89.778 | 93.958 |

Productivity Factor | Correlation | Principal Component Analysis | |||
---|---|---|---|---|---|

Pearson Correlation Set A | PC1 Set B | PC1–PC2 Set C | PC1–PC5 Set D | Biplot Set E | |

Number of Masons | x | x | x | x | |

Number of Helpers | x | x | |||

Mason Wages | x | ||||

Helper Wages | |||||

Mason Competency | x | x | |||

Weather | x | x | x | x | |

Workday Duration | |||||

Wall Length | x | ||||

Wall Height | x | x | x | x | |

Total Features Selected | 3 | 2 | 3 | 6 | 4 |

Variable | Boolean | Euclidean Distance |
---|---|---|

Number of Masons | TRUE | 0.772 |

Number of Helpers | TRUE | 0.965 |

Mason Wages | FALSE | 0.218 |

Helper Wages | FALSE | 0.120 |

Mason Competency | TRUE | 0.934 |

Weather | TRUE | 0.980 |

Workday Duration | FALSE | 0.231 |

Wall Length | FALSE | 0.344 |

Wall Height | FALSE | 0.637 |

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## Share and Cite

**MDPI and ACS Style**

Ekyalimpa, R.; Okello, E.; Siraj, N.B.; Lei, Z.; Liu, H.
Towards Human–Robot Collaboration in Construction: Understanding Brickwork Production Rate Factors. *Buildings* **2023**, *13*, 3087.
https://doi.org/10.3390/buildings13123087

**AMA Style**

Ekyalimpa R, Okello E, Siraj NB, Lei Z, Liu H.
Towards Human–Robot Collaboration in Construction: Understanding Brickwork Production Rate Factors. *Buildings*. 2023; 13(12):3087.
https://doi.org/10.3390/buildings13123087

**Chicago/Turabian Style**

Ekyalimpa, Ronald, Emmanuel Okello, Nasir Bedewi Siraj, Zhen Lei, and Hexu Liu.
2023. "Towards Human–Robot Collaboration in Construction: Understanding Brickwork Production Rate Factors" *Buildings* 13, no. 12: 3087.
https://doi.org/10.3390/buildings13123087