# 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

- Latorella, K.A.; Prabhu, P.V. A review of human error in aviation maintenance and inspection. Int. J. Ind. Ergonom.
**2000**, 26, 133–161. [Google Scholar] [CrossRef] - Regulation L 13 Investigation of Accidents and Incidents, Ministry of Transport of the Slovak Republic; Air traffic services of the Slovak Republic: Bratislava, Slovakia, 2007.
- Annex 13 To the Convention on International Civil Aviation Aircraft Accident and Incident Investigation. Available online: https://www.emsa.europa.eu/retro/Docs/marine_casualties/annex_13.pdf (accessed on 13 April 2021).
- Annual Safety Review 2019. Available online: https://www.easa.europa.eu/sites/default/files/dfu/Annual%20Safety%20Review%202019.pdf (accessed on 13 April 2021).
- Balicki, W.; Głowacki, P.; Loroch, L. Large aircraft reliability study as important aspect of the aircraft systems’ design changes and improvements. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng.
**2020**. [Google Scholar] [CrossRef] - Janic, M. An assessment of risk and safety in civil aviation. J. Air Transp. Manag.
**2000**, 6, 43–50. [Google Scholar] [CrossRef] - Saleh, J.H.; Marais, K.B.; Bakolas, E.; Cowlagi, R.V. Highlights from the literature on accident causation and system safety: Review of major ideas, recent contributions, and challenges. Reliab. Eng. Syst. Safe
**2010**, 95, 1105–1116. [Google Scholar] [CrossRef] - Kharoufah, H.; Murray, J.; Baxter, G.; Wild, G. A review of human factors causations in commercial air transport accidents and incidents: From to 2000–2016. Prog. Aerosp. Sci.
**2018**, 99, 1–13. [Google Scholar] [CrossRef] - The Nall Report 2007: Accidents Trends and Factors for 2006. Available online: https://www.aopa.org/-/media/Files/AOPA/Home/Training-and-Safety/Nall-Report/07nall.pdf (accessed on 13 April 2021).
- Caldwell, J. Crew schedules, sleep deprivation, and aviation performance. SAGE J.
**2012**, 21, 85–89. [Google Scholar] [CrossRef] - Lin, P.H.; Hale, A.R.; Van Gulijk, C.; Ale, B.J.M.; Roelen, A.L.C.; Bellamy, L.J. Testing a safety management system in aviation. In Proceedings of the 9th International Conference on Probabilistic Safety Assessment and Management 2008, Hong Kong, China, 18–23 May 2008. Code 96615. [Google Scholar]
- Koščák, P.; Berežný, S.; Vajdová, I.; Koblen, I.; Ojciec, M.; Matisková, D.; Puškáš, T. Reducing the negative environmental impact of winter airport maintenance through its model design and simulation. Int. J. Environ. Res. Pub. Health
**2020**, 17, 1296. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Li, W.C.; Harris, D. Routes to failure: Analysis of 41 civil aviation accidents from the Republic of China using the human factors analysis and classification system. Accid. Anal. Prev.
**2008**, 40, 426–434. [Google Scholar] [CrossRef] [PubMed] - Marais, K.B.; Robichaud, M.R. Analysis of trends in aviation maintenance risk: An empirical approach. Reliab. Eng. Syst. Saf.
**2012**, 106, 104–118. [Google Scholar] [CrossRef] - Burmistrova, V.G.; Butov, A.A.; Volkov, M.A.; Yavtushenko, M.S.; Kostishko, B.M.; Moskvicheva, M.G.; Pchelkina, Y.Z. The change in the probability of aviation accidents “collision of an aircraft with a bird” in accordance with of a change in the temperature cycle. Journal of Physics: Conference Series, Volume 1745. In Proceedings of the VI International Conference on Information Technology and Nanotechnology (ITNT-2020), Samara, Russia, 26–29 May 2020. Code 167456. [Google Scholar]
- Insley, J.; Turkoglu, C.A. Contemporary Analysis of Aircraft Maintenance-Related Accidents and Serious Incidents. Aerospace
**2020**, 7, 81. [Google Scholar] [CrossRef] - Roelen, A.L.C.; Lin, P.H.; Hale, A.R. Accident models and organisational factors in air transport: The need for multi-method models. Saf. Sci.
**2011**, 49, 5–10. [Google Scholar] [CrossRef] - Roelen, A.; Wever, R.; Mosleh, A.; Groth, K. Development and validation of a comprehensive hybrid causal model for safety assessment and management of aviation systems. In Proceedings of the 9th International Conference on Probabilistic Safety Assessment and Management 2008, Hong Kong, China, 18–23 May 2008. Code 96615. [Google Scholar]
- Ale, B.J.M.; Bellamy, L.J.; Van Der Boom, R.; Cooper, J.; Cooke, R.M.; Goossens, L.H.J.; Hale, A.R.; Kurowicka, D.; Morales, O.; Roelen, A.L.C.; et al. Further development of a Causal model for Air Transport Safety (CATS): Building the mathematical heart. Reliab. Eng. Syst. Safe
**2009**, 94, 1433–1441. [Google Scholar] [CrossRef] - Leveson, N. A new accident model for engineering safer systems. Saf. Sci.
**2004**, 42, 237–270. [Google Scholar] [CrossRef] [Green Version] - Blom, H.A.P.; Bloem, E.A. Modeling and estimation of accident rate and trend in air transport. In Proceedings of the 13th Conference on Information Fusion, Fusion 2010, Edinburgh, UK, 26–29 July 2010. Article number 5711871. [Google Scholar] [CrossRef]
- Chen, J.C.; Lin, S.C.; Yu, W.F. Structuring an effective human error intervention strategy selection model for commercial aviation. J. Air Transp. Manag.
**2017**, 60, 65–75. [Google Scholar] [CrossRef] - Zhang, X.; Mahadevan, S. Bayesian network modeling of accident investigation reports for aviation safety assessment. Reliab. Eng. Syst. Safe
**2021**, 209. [Google Scholar] [CrossRef] - Cheng, S.Z.Y.L.; Valdés, R.M.A.; Comendador, V.F.G.; Nieto, F.J.S. Detection of common causes between air traffic serious and major incidents in applying the convolution operator to Heinrich pyramid theory. Entropy
**2019**, 21, 1166. [Google Scholar] [CrossRef] [Green Version] - Boyd, D.D.; Howell, C. Accident rates, causes, and occupant injury involving high-performance general aviation aircraft. Aerosp Med. Hum. Perf.
**2020**, 91, 387–393. [Google Scholar] [CrossRef] - Mannering, F.L.; Bhat, C.H.R. Analytic methods in accident research: Methodological frontier and future directions. Anal. Methods Accid. Res.
**2014**, 1, 1–22. [Google Scholar] [CrossRef] - Fardnia, P.; Kaspereit, T.; Walker, T.; Xu, S. Financial performance and safety in the aviation industry. Int. J. Manag. Financ.
**2020**, 17, 138–165. [Google Scholar] [CrossRef] - Brown, A.S. The effects of airline behavior on aircraft accidents. Gettysbg. Econ. Rev.
**2017**, 10, 70–105. [Google Scholar] - Li, Z.; Wang, W.; Liu, P.; Bigham, J.M.; Ragland, D.R. Using geographically weighted Poisson regression for county-level crash modeling in California. Saf. Sci.
**2013**, 58, 89–97. [Google Scholar] [CrossRef] - Al-Hasani, G.; Asaduzzaman, M.; Soliman, A.H. Comparison of Spatial Regression Models with Road Traffic Accidents Data. In Proceedings of the International Conference on Statistic: Theory and Applications, Lisbon, Portugal, 13–14 August 2019. Paper No. 31. [Google Scholar] [CrossRef]
- Salvagioni, D.A.J.; Mesas, A.E.; Melanda, F.N.; dos Santos, H.G.; González, A.D.; Girotto, E.; de Andrade, S.M. Prospective association between burnout and road traffic accidents in teachers. Stress Health
**2020**, 36, 629–638. [Google Scholar] [CrossRef] - Sajed, Y.; Shafabakhsh, G.; Bagheri, M. Hotspot location identification using accident data, traffic and geometric characteristics. Eng. J. Can.
**2019**, 23, 191–207. [Google Scholar] [CrossRef] - Gildea, K.M.; Hileman, C.R.; Rogers, P.; Salazar, G.J.; Paskoff, L.N. The use of a poisson regression to evaluate antihistamines and fatal aircraft mishaps in instrument meteorological conditions. Aerosp. Med. Hum. Perf.
**2018**, 89, 389–395. [Google Scholar] [CrossRef] - Strategic Transport Development Plan of the Slovak Republic up to 2030–Phase II; Ministry of Transport, Construction and Regional Development of the Slovak Republic: Bratislava, Slovakia, 2016.
- List of Airports and Heliports. Transport Authority. Available online: http://letectvo.nsat.sk/airporta-a-stavby/airporta/zoznam-airport-a-heliportov/ (accessed on 13 April 2021).
- Civil Aviation Accidents and Incidents. Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=LEGISSUM:tr0046 (accessed on 13 April 2021).
- Statistics in Civil Aviation Report. Ministry of Transport, Construction and Regional Development of the Slovak Republic. Available online: https://www.mindop.sk/ (accessed on 13 April 2021).
- ICAO Emergency Phases—SKYbrary Aviation Safety. Available online: https://www.skybrary.aero/index.php/ICAO_Emergency_Phases (accessed on 13 April 2021).
- Eurostat Database. Available online: https://ec.europa.eu/eurostat/data/database (accessed on 13 April 2021).
- STATdat. Public Database. Available online: http://statdat.statistics.sk (accessed on 13 April 2021).
- Montgomery, D.C. Introduction to Statistical Quality Control, 6th ed.; John Wiley & Sons: New York, NY, USA, 2009; pp. 199–202. [Google Scholar]
- Agresti, A. An Introduction to Categorical Data Analysis, 3rd ed.; John Wiley & Sons: Hoboken, NJ, USA, 2019; pp. 63–83. [Google Scholar]
- Cameron, A.C.; Windmeijer, F.F.G. R-Squared Measures for Count Data Regression Models with Applications to Health Care Utilization. J. Bus. Econ. Stat.
**1996**, 14, 209–220. [Google Scholar] [CrossRef] - Roback, P.; Legler, J. Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R, 1st ed.; CRC Press: New York, NY, USA, 2021. [Google Scholar]

**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