# Civil Aviation Occurrences in Slovakia and Their Evaluation Using Statistical Methods

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Accident Rates in Slovakia

#### 2.2. Civil Aviation Occurrences

#### 2.3. Statistical Methods

#### 2.3.1. Hypothesis Testing

#### 2.3.2. Pareto Analysis

#### 2.3.3. Multiple Linear Regression

^{2}. The coefficient values ranged within the interval 〈0;1〉. As the value approached 1, the correlation was stronger.

#### 2.3.4. Poisson Regression Model

^{2}, as it is in the multiple regression analysis. A degree of the correlation between variable Y and explanatory variables in the Poisson regression was determined using the pseudo R

^{2}for Poisson regression, which may be interpreted similarly to r

^{2}[43]. All data were evaluated, and the results were obtained using the R package software [44].

## 3. Results and Discussion

- Analysing civil aviation occurrences for the period from 2000 to 2019;
- Determining the key categories of incidents that largely affect the occurrence of incidents in civil aviation;
- Modelling a correlation between the civil aviation occurrences (CAOs) and selected input variables by applying the multiple and Poisson regressions.

#### 3.1. Analysis of Civil Aviation Occurrences for the Period from 2000 to 2019

#### 3.2. Determination of the Key Categories of Civil Aviation Incidents in Slovakia

#### 3.3. Modelling the Number of CAOs Depending on Selected Parameters

#### 3.3.1. Classical Regression Model (Model I)

_{4}(Civil Planes) and X

_{7}(Movement), had statistically significant effects on the number of CAOs. The equation of the best regression model is as follows:

#### 3.3.2. Poisson Regression Model (Model II)

_{1}(Year), X

_{4}(Civil Planes), X

_{6}(Age) and X

_{7}(Movement) had statistically significant effects on the number of CAOs. It seems that the best resulting model is as follows:

^{2}value was 0.909; this means that the model explains 90.9% of the variability of the dependent variable CAOs, which is explained by the input variables. A positive value of coefficient ${\beta}_{i}$ means that as the value of variable ${X}_{i}$ increases by 1 (with the remaining variables unchanged), the expected variable CAOs increase. A negative value of coefficient ${\beta}_{i}$ indicates that if the Xi value increases by 1 (with the remaining variables unchanged), the expected value of CAOs decreases.

_{1}(Year) changes by one unit and the values of the remaining input variables remain fixed, the expected number of CAOs will be exp(0.029) = 1.029 times higher than the value at the unchanged variable X

_{1}(there will be an increase by 2.9%). This means that the number of aviation occurrences increases annually by 2.9% on average. If the value of input variable X

_{4}(Civil Planes) changes by one unit and the values of the remaining input variables remain fixed, the expected number of CAOs will be exp(−0.008) = 0.99 times lower than the value at the unchanged variable X

_{4}(there will be almost a negligible 1% decrease in the number of occurrences). An increase in variable X

_{6}(Age) by 1, with the remaining variables unchanged, will cause an increase in the expected number of CAOs by 3.9% (exp(0.039) = 1.039 > 1). This means that if the number of commercial aircrafts aged over 14 years increases by 1 (with the remaining variables unchanged), the number of aviation occurrences will increase by 3.9%. The same applies to variable X

_{7}(Movement, in thousands). An increase in variable X

_{7}by 1 (with the remaining variables unchanged) will also cause a very slight increase in the expected number of CAOs by 3.1% (exp(0.031) = 1.031 > 1). When the total number of aircraft movements increases by 1 (in thousands), there will be an increase in the number of aviation occurrences by 3.1%.

#### 3.3.3. Comparison of Models

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Aviation accidents, the number of fatalities and injuries in civil aviation accidents (period 2000–2019).

Characteristics | Transport | ||
---|---|---|---|

Air | Road | Railway | |

Number for the entire period | 150 | 172,173 | 999 |

Maximum value | 26 | 25,989 | 190 |

Minimum value | 6 | 13,307 | 60 |

Average number per year | 13.64 | 15,652.09 | 90.82 |

Standard deviation | 6.772 | 4169.01 | 36.989 |

**Table 2.**Descriptive statistics of the number of fatal or serious injuries for the period of 2009–2019.

Characteristics | Number of Injuries in Traffic Accidents | |||||
---|---|---|---|---|---|---|

Air Transport | Road Transport | Railway Transport | ||||

Fatal | Serious | Fatal | Serious | Fatal | Serious | |

Number for the entire period | 29 | 37 | 3034 | 12,716 | 550 | 411 |

Maximum value | 7 | 7 | 347 | 1408 | 78 | 45 |

Minimum value | 0 | 0 | 223 | 1050 | 26 | 33 |

Average number per year | 2.64 | 3.36 | 275.82 | 1156 | 50 | 37.36 |

Standard deviation | 2.06 | 2.34 | 45.40 | 105.94 | 19.42 | 3.83 |

Incident Category | Incident Category | ||
---|---|---|---|

I1 | Loss of communication during the flight | I10 | Unauthorised penetration of airspace |

I2 | Loss of communication | I11 | Failure or malfunction of an aircraft system |

I3 | Occurrences involving collisions/near collisions with bird(s)/wildlife | I12 | Declared Incerfa, Alerfa, Detresfa |

I4 | Safety landing | I13 | Occurrences involving ATM or ATS |

I5 | Emergency landing | I14 | Laser |

I6 | Loss of separation | I15 | Loss of aircraft control while the aircraft is on the ground |

I7 | STCA, ACAS, MSAW, APW, GPWS, A-SMGCS | I16 | Miscellaneous occurrences in the passenger cabin |

I8 | ACFT deviation from the ATM approval or from the planned ATC procedures | I17 | Medical emergency |

I9 | Runway Incursion | I18 | Illegal radio broadcasting |

Year | AA | SI | I | GI | Year | AA | SI | I | GI |
---|---|---|---|---|---|---|---|---|---|

2000 | 36.4 | 34.1 | 9.1 | 20.5 | 2010 | 6.3 | 0.5 | 60.5 | 32.8 |

2001 | 35.0 | 35.0 | 22.5 | 7.5 | 2011 | 4.6 | 0.8 | 66.4 | 28.2 |

2002 | 29.1 | 23.6 | 36.4 | 10.9 | 2012 | 4.4 | 1.1 | 56.9 | 37.5 |

2003 | 27.3 | 17.0 | 52.3 | 3.4 | 2013 | 4.2 | 3.4 | 89.3 | 3.1 |

2004 | 27.0 | 21.6 | 51.4 | 0.0 | 2014 | 2.6 | 0.7 | 95.6 | 1.1 |

2005 | 7.1 | 4.0 | 84.8 | 4.0 | 2015 | 2.5 | 1.1 | 96.1 | 0.3 |

2006 | 10.2 | 3.6 | 83.2 | 3.0 | 2016 | 3.6 | 0.7 | 95.7 | 0.0 |

2007 | 10.6 | 1.0 | 79.8 | 8.6 | 2017 | 4.2 | 0.8 | 93.8 | 1.2 |

2008 | 8.2 | 4.1 | 65.3 | 22.4 | 2018 | 1.7 | 0.0 | 94.8 | 3.5 |

2009 | 6.1 | 2.2 | 56.5 | 35.1 | 2019 | 3.3 | 0.0 | 94.2 | 2.5 |

Characteristics | Incident Category [Number] | ||||||||
---|---|---|---|---|---|---|---|---|---|

I1 | I2 | I3 | I4 | I5 | I6 | I7 | I8 | I9 | |

Number for the whole period | 267 | 57 | 607 | 19 | 19 | 61 | 96 | 191 | 13 |

Maximum value | 44 | 13 | 78 | 7 | 5 | 14 | 45 | 46 | 5 |

Minimum value | 11 | 1 | 35 | 0 | 0 | 0 | 2 | 9 | 0 |

Average number per year | 26.70 | 5.70 | 60.70 | 2.38 | 2.38 | 6.10 | 9.60 | 19.1 | 2.17 |

Standard deviation | 10.10 | 3.80 | 12.91 | 2.45 | 1.85 | 3.70 | 13.01 | 10.79 | 1.72 |

Percentage for the monitored period [%] | 12.19 | 2.60 | 27.72 | 0.87 | 0.87 | 2.79 | 4.38 | 8.72 | 0.59 |

Characteristics | I10 | I11 | I12 | I13 | I14 | I15 | I16 | I17 | I18 |

Number for the whole period | 197 | 343 | 50 | 3 | 237 | 13 | 5 | 9 | 3 |

Maximum value | 44 | 60 | 22 | 2 | 37 | 4 | 2 | 3 | 2 |

Minimum value | 7 | 20 | 1 | 0 | 22 | 1 | 0 | 1 | 0 |

Average number per year | 28.14 | 38.11 | 5.56 | 0.50 | 29.63 | 2.60 | 0.83 | 1.80 | 0.60 |

Standard deviation | 11.91 | 10.79 | 6.67 | 0.84 | 5.95 | 1.14 | 0.75 | 0.84 | 0.89 |

Percentage for the monitored period [%] | 9.00 | 15.67 | 2.28 | 0.14 | 10.82 | 0.59 | 0.23 | 0.41 | 0.14 |

Variables | Description |
---|---|

Dependent Variables | |

CAO (Y) | Number of CAOs in a given year |

Independent Variables | |

Year (X_{1}) | Time variable, Year = 1 for year 2009, ..., Year = 10 for year 2018 |

Passenger (X_{2}) | Number of passengers transported in Slovakia in a given year (in mil.) |

Goods (X_{3}) | Amount of transported goods in a given year (in thousands of tonnes) |

Civil Planes (X_{4}) | Number of all civil planes registered in Slovakia in a given year |

Aircraft (X_{5}) | Number of commercial aircraft with the weight of 9000 kg and more in a given year |

Age (X_{6}) | Number of commercial aircraft with the weight of 9000 kg and more and aged over 14 years in a given year |

Movement (X_{7}) | Number of landings or takeoffs at airports in a given year (in thousands) |

Coefficient | Estimate | Standard Error | p-Value | 95% Confidence Interval |
---|---|---|---|---|

Intercept | 1302.904 | 356.161 | 0.008 | (604.841; 2000.967) |

Civil Planes (β_{4}) | −1.993 | 0.543 | 0.008 | (−3.058; −0.928) |

Movement (β_{7}) | 7.792 | 1.919 | 0.005 | (4.031; 11.552) |

Coefficient | Estimate | Standard Error | p-Value | 95% Confidence Interval |
---|---|---|---|---|

Intercept | 11.043 | 0.823 | 2 × 10^{−16} | (9.427; 12.63) |

Year (β_{1}) | 0.029 | 0.012 | 1 × 10^{−2} | (0.005; 0.052) |

Civil Planes (β_{4}) | −0.011 | 0.001 | 4 × 10^{−13} | (−0.014; −0.008) |

Age (β_{6}) | 0.035 | 0.011 | 2 × 10^{−3} | (0.012; 0.057) |

Movement (β_{7}) | 0.038 | 0.004 | 2 × 10^{−16} | (0.029; 0.046) |

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**MDPI and ACS Style**

Andrejiova, M.; Grincova, A.; Marasova, D.; Koščák, P.
Civil Aviation Occurrences in Slovakia and Their Evaluation Using Statistical Methods. *Sustainability* **2021**, *13*, 5396.
https://doi.org/10.3390/su13105396

**AMA Style**

Andrejiova M, Grincova A, Marasova D, Koščák P.
Civil Aviation Occurrences in Slovakia and Their Evaluation Using Statistical Methods. *Sustainability*. 2021; 13(10):5396.
https://doi.org/10.3390/su13105396

**Chicago/Turabian Style**

Andrejiova, Miriam, Anna Grincova, Daniela Marasova, and Peter Koščák.
2021. "Civil Aviation Occurrences in Slovakia and Their Evaluation Using Statistical Methods" *Sustainability* 13, no. 10: 5396.
https://doi.org/10.3390/su13105396