# Anticipating the Length of Employees’ Working Time

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### Methods

_{i}—actual value of the variable in period i; Y

_{ip}—projected value of the variable in period i.

## 3. Results

#### 3.1. Multiple Regresion Method

#### 3.1.1. MR1

#### 3.1.2. MR2

#### 3.2. Multivariate Adaptive Regression Splines Method

#### 3.3. Generalized Additive Models Method

#### 3.3.1. GAM1

#### 3.3.2. GAM2

#### 3.4. Neural Networks Method

## 4. Discussion

## 5. Conclusions

- (1)
- Forecasting and prediction is possible based on the regression formula of employee performance by the MMSM method. The method shows how certain characteristic variables for this process have an impact on the duration of works;
- (2)
- Half of the analyzed models is correct and reflects employee performance very accurately. It is possible to use selected models to assess employee performance and the duration of work for a specific order;
- (3)
- The best forecast was obtained using the automatic neural network method, MAPE = 0.02%. The disadvantage of this method is the lack of a regression pattern, which limits its universality. New calculations can be made by a person who has all previous data and a neural network.

## Author Contributions

## Funding

## Conflicts of Interest

## Signs

MMSM | Multivariate Method of Statistical Models |

MR | Multiple Regresion |

MARS | Multivariate Adaptive Regression Splines |

GAM | Generalized Additive Models |

NN | Neural Networks |

MAPE | Mean Absolute Percentage Error |

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**Figure 1.**Correlation between employee productivity, employee experience and number of elements made.

Employee Productivity [pcs/h] | Employee Experience [years] | Number of Elements Made [pcs] | Failure/Equipment Repair [%] | Temp. [°C] | Grinding Time [h] | Well-Being Assessment [1–5] | |
---|---|---|---|---|---|---|---|

Day 1 | 2.10 | 1 | 15.75 | 3.5 | 21 | 4 | 3 |

2.13 | 3 | 16.00 | 3 | 21 | 3.25 | 3 | |

2.23 | 4 | 16.75 | 5 | 21 | 3 | 4 | |

2.20 | 5 | 16.50 | 4.5 | 21 | 3.25 | 4 | |

2.20 | 5 | 16.50 | 5.5 | 21 | 3 | 5 | |

2.30 | 7 | 17.25 | 4 | 21 | 3.25 | 3 | |

2.30 | 7 | 17.25 | 4.3 | 21 | 3.25 | 3 | |

2.40 | 9 | 18.00 | 4.3 | 21 | 3.25 | 5 | |

Day 2 | 2.10 | 1 | 15.75 | 3.5 | 21.5 | 3.5 | 4 |

2.13 | 3 | 16.00 | 3 | 21.5 | 3.75 | 4 | |

2.20 | 4 | 16.50 | 5 | 21.5 | 3 | 4 | |

2.23 | 5 | 16.75 | 4.5 | 21.5 | 3.25 | 3 | |

2.27 | 5 | 17.00 | 5.5 | 21.5 | 3 | 4 | |

2.30 | 7 | 17.25 | 4 | 21.5 | 3.25 | 3 | |

2.30 | 7 | 17.25 | 4.3 | 21.5 | 3.25 | 4 | |

2.37 | 9 | 17.75 | 4.3 | 21.5 | 2.75 | 3 | |

Day 3 | 2.13 | 1 | 16.00 | 3.5 | 20.5 | 3.25 | 4 |

2.13 | 3 | 16.00 | 3 | 20.5 | 3.75 | 3 | |

2.20 | 4 | 16.50 | 5 | 20.5 | 3.5 | 2 | |

2.23 | 5 | 16.75 | 4.5 | 20.5 | 3.25 | 3 | |

2.27 | 5 | 17.00 | 5.5 | 20,5 | 3.25 | 4 | |

2.27 | 7 | 17.00 | 4 | 20.5 | 3 | 2 | |

2.33 | 7 | 17.50 | 4.3 | 20.5 | 2.75 | 3 | |

2.40 | 9 | 18.00 | 4.3 | 20.5 | 3 | 4 | |

Day 4 | 2.10 | 1 | 15.75 | 3.5 | 21 | 3.5 | 3 |

2.20 | 3 | 16.50 | 3 | 21 | 3.5 | 4 | |

2.20 | 4 | 16.50 | 5 | 21 | 3 | 3 | |

2.23 | 5 | 16.75 | 4.5 | 21 | 3.25 | 3 | |

2.27 | 5 | 17.00 | 5.5 | 21 | 2.75 | 4 | |

2.30 | 7 | 17.25 | 4 | 21 | 3.25 | 3 | |

2.30 | 7 | 17.25 | 4.3 | 21 | 2.75 | 4 | |

2.40 | 9 | 18.00 | 4.3 | 21 | 2.5 | 3 |

No. | Variable Name | Chart | W |
---|---|---|---|

v1 | Employee productivity [pcs/h] | 0.948 | |

v2 | Employee experience [years] | 0.930 | |

v3 | Number of elements made [pcs] | 0.948 | |

v4 | Failure/equipment repair [%] | 0.933 | |

v5 | Temp. [°C] | 0.810 | |

v6 | Grinding time [h] | 0.938 | |

v7 | Well-being assessment | 0.839 |

Variable | Correlations Marked Correlations are Significant at p < 0.05000 N = 32 (Casewise Deletion of Missing Data) CumulativePe | ||||||||
---|---|---|---|---|---|---|---|---|---|

Means | Std.Dev. | Employee Productivity [pcs/h] | Employee Experience [years] | Number of Elements Made [pcs] | Failure/Equipment Repair [%] | Temp. [℃] | Grinding Time [h] | Well-Being Assessment [1–5] | |

Employee productivity [pcs/h] | 2.242 | 0.088 | 1.000 | 0.965 | 1.000 | 0.379 | −0.034 | −0.676 | 0.055 |

Employee experience [years] | 5.125 | 2.406 | 0.965 | 1.000 | 0.965 | 0.324 | 0.000 | −0.636 | −0.016 |

Number of elements made [pcs] | 16.813 | 0.660 | 1.000 | 0.965 | 1.000 | 0.379 | −0.034 | −0.676 | 0.055 |

Failure/equipment repair [%] | 4.263 | 0.752 | 0.379 | 0.324 | 0.379 | 1.000 | 0.000 | −0.555 | 0.213 |

Temp. [°C] | 21.000 | 0.359 | −0.034 | 0.000 | −0.034 | 0.000 | 1.000 | 0.000 | 0.250 |

Grinding time [h] | 3.195 | 0.322 | −0.676 | −0.636 | −0.676 | −0.555 | 0.000 | 1.000 | −0.095 |

Well-being assessment [1–5] | 3.469 | 0.718 | 0.055 | −0.016 | 0.055 | 0.213 | 0.250 | −0.095 | 1.000 |

MR1 (v1; v2, v5, v6, v7) Dependent Variable: v1; Independent Variable: v2, v5, v6, v7 | ||||||
---|---|---|---|---|---|---|

N = 32 | Regression Summary for Dependent Variable: Employee Productivity [pcs/h] R = 0.97151969 R2 = 0.94385051 Adjusted R2 = 0.93553207 F(4.27) = 113.46 p < 0.00000 Std.Error of estimate: 0.02234 | |||||

Beta | Std. Err. of Beta | B | Std. Err. of B | t (27) | p-Level | |

Intercept | 2.390392 | 0.244150 | 9.79067 | 0.000000 | ||

v2 | 0.908220 | 0.059407 | 0.033210 | 0.002172 | 15.28803 | 0.000000 |

v6 | −0.091091 | 0.059686 | −0.024881 | 0.016303 | −1.52617 | 0.138598 |

v7 | 0.074736 | 0.047582 | 0.009162 | 0.005833 | 1.57067 | 0.127906 |

v5 | −0.052723 | 0.047132 | −0.012914 | 0.011545 | −1.11863 | 0.273151 |

MR2 (v1; Log(v3), v4, v7) Dependent Variable: v1; Independent Variable: Log(v3), v4, v7 | ||||||
---|---|---|---|---|---|---|

N = 32 | Regression Summary for Dependent Variable: Employee Productivity [pcs/h] R = 0.99984602 R2 = 0.99969206 Adjusted R2 = 0.99965907 F(3.28) = 30300, p < 0.0000 Std.Error of Estimate: 0.00162 | |||||

Beta | Std. Err. of Beta | B | Std. Err. of B | t (27) | p-Level | |

Intercept | −4.11047 | 0.022218 | −185.009 | 0.000000 | ||

Log(v3) | 1.004722 | 0.003602 | 2.25307 | 0.008078 | 278.909 | 0.000000 |

v4 | −0.013375 | 0.003682 | −0.00157 | 0.000431 | −3.633 | 0.001114 |

v7 | 0.004819 | 0.003396 | 0.00059 | 0.000416 | 1.419 | 0.166949 |

Model Specifications | Model Summary |
---|---|

Value | |

Independents | 5 |

Dependents | 1 |

Number of terms | 2 |

Number of basis functions | 1 |

Order of interactions | 1 |

Penalty | 2.000000 |

Threshold | 0.000500 |

GCV error | 0.000629 |

Prune | Yes |

Dependents | Number of References to Each Predictor Number of Times Each Predictor is Referenced (Used) |
---|---|

References | |

Employee experience [years] | 1 |

Failure/equipment repair [%] | 0 |

Temperature [°C] | 0 |

Grinding time [h] | 0 |

Well-being assessment [1–5] | 0 |

Coefficients, Knots and Basis Functions | Model Coefficients NOTE: Highlighted Cells Indicate Basis Functions of Type Max(0, Independent-Knot), otherwise Max(0, Knot-Independent) | ||||||
---|---|---|---|---|---|---|---|

Coefficients v1 | Knots v2 | Knots v3 | Knots v4 | Knots v5 | Knots v6 | Knots v7 | |

Intercept | 2.096123 | - | - | - | - | - | - |

Term.1 | 0.035283 | 1.00 | - | - | - | - | - |

Variable Index | Degrees of Freedom | GAM Coefficient | Std. Err. | Result Std. | p-Level | |
---|---|---|---|---|---|---|

Intercept | 0 | 1.000000 | −0.020311 | 0.012648 | −1.6058 | |

v2 | 1 | 3.999711 | −0.000897 | 0.000204 | −4.3932 | 0.000000 |

v3 | 2 | 3.998411 | 0.134833 | 0.000779 | 173.1406 | 0.000000 |

v4 | 3 | 4.001388 | 0.000079 | 0.000206 | 0.3823 | 0.000000 |

v6 | 4 | 4.000114 | −0.000198 | 0.000595 | −0.3329 | 0.933869 |

Variable Index | Degrees of Freedom | GAM Coefficient | Std. Err. | Result Std. | p-Level | |
---|---|---|---|---|---|---|

Intercept | 0 | 1.000000 | −0.193360 | 0.001631 | −118.549 | |

v2 | 1 | 3.999711 | −0.000019 | 0.000026 | −0.703 | 0.000000 |

v3 | 2 | 3.998411 | 0.059500 | 0.000100 | 592.487 | 0.000000 |

v4 | 3 | 4.001388 | −0.000024 | 0.000027 | −0.919 | 0.948296 |

v6 | 4 | 4.000114 | −0.000096 | 0.000077 | −1.255 | 0.580771 |

Index | Net. Name | Training Perf. | Test Perf. | Training Error | Test Error |
---|---|---|---|---|---|

1 | MLP 6-7-1 | 0.999985 | 0.999991 | 0.000002 | 0.000002 |

Training Algorithm | Error Function | Hidden Activation | Output Activation |
---|---|---|---|

BFGS 17 | SOS | Tanh | Identity |

Method Name | Autocorrelation of Residues or Partial Residues | Model Correctness | MAPE Error [%] |
---|---|---|---|

MR1 (v1; v2, v5, v6, v7) | Does not occur | Correct | 0.72 |

MR2 (v1; Log(v3), v4, v7) | In 6th place | Incorrect | - |

MARS1 (v1; v2, v4, v5, v6, v7) | Does not occur | Correct | 0.82 |

GAM1 (v1; v2, v3, v4, v6 | In 4th place | Incorrect | - |

GAM2 (v1; v2, v3, v4, v5, v6, v7) | In 8th place | Incorrect | - |

NN1 (v1; v2, v3, v4, v5, v6, v7) | In 12th place | Correct | 0.02 |

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## Share and Cite

**MDPI and ACS Style**

Kostrzewa-Demczuk, P.; Rogalska, M.
Anticipating the Length of Employees’ Working Time. *Symmetry* **2020**, *12*, 413.
https://doi.org/10.3390/sym12030413

**AMA Style**

Kostrzewa-Demczuk P, Rogalska M.
Anticipating the Length of Employees’ Working Time. *Symmetry*. 2020; 12(3):413.
https://doi.org/10.3390/sym12030413

**Chicago/Turabian Style**

Kostrzewa-Demczuk, Paulina, and Magdalena Rogalska.
2020. "Anticipating the Length of Employees’ Working Time" *Symmetry* 12, no. 3: 413.
https://doi.org/10.3390/sym12030413