Civil Aviation Occurrences in Slovakia and Their Evaluation Using Statistical Methods

sustainability

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

Miriam Andrejiova 1 , Anna Grincova 2,* , Daniela Marasova 3 and Peter Košˇcák 4

1 Faculty of Mechanical Engineering, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovakia; [email protected] 2 Faculty of Electrical Engineering and Informatics, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovakia 3 Faculty of Mining, Ecology, Process Control and Geotechnology, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovakia; [email protected] 4 Faculty of Aeronautics, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovakia; [email protected] * Correspondence: [email protected]

Abstract: The nature of a civil aviation occurrence may be defined in three different categories while considering its severity. General categories include civil aviation accidents, serious incidents and incidents. The present article analyses the civil aviation occurrences in Slovakia which happened in the period from 2000 to 2019. In this period, there was a significant increase in the number of civil aviation occurrences, and incidents, in particular, represented the highest percentage. A Pareto analysis was applied to identify the key incident categories (wildlife strike, technical failures of the aviation technology and unauthorised penetration of airspace). A multiple regression analysis and the Poisson regression were used to create two models of correlations between the number of civil aviation occurrences and the selected input variables. Both models are statistically significant, and, based on the AIC (Akaike Information Criterion), the Poisson regression model appeared to be of higher quality. The model showed, for example, that an increase in variables (the number of Citation: Andrejiova, M.; Grincova, commercial aircrafts aged over 14 years and the number of total aircraft movements) resulted in a A.; Marasova, D.; Košˇcák,P. Civil slight increase in the expected number of civil aviation occurrences. Aviation Occurrences in Slovakia and Their Evaluation Using Statistical Keywords: civil aviation; occurrence; incidents; regression models Methods. Sustainability 2021, 13, 5396. https://doi.org/10.3390/su13105396

Academic Editor: Lynnette Dray 1. Introduction Civil aviation is currently the safest, fastest and most comfortable mode of transport. Received: 21 April 2021 This is a result of strict safety regulations governing the piloting, air trafﬁc and aviation Accepted: 10 May 2021 Published: 12 May 2021 technology maintenance. According to the recommendations of the International Air Transport Association, the demand for civil aviation services is expected to double over

Publisher’s Note: MDPI stays neutral the following two decades. This would, however, bring more problems to the field of with regard to jurisdictional claims in aviation safety as a result of increased air transport congestion and more load put on the published maps and institutional affil- civil aviation system. iations. Aviation safety is significantly affected by the constant development of novel technologies [1]. However, despite the well thought-out technical and safety precautions, civil aviation occurrences still happen. According to [2,3], a civil aviation occurrence (CAO) is defined as an occurrence associated with the operation of an aircraft that affects or could affect the air traffic safety, and which is due to its consequences assessed as an aviation Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. accident, serious incident, incident or ground incident. The Annual Safety Review [4] This article is an open access article stated that the accident rate has been constantly decreasing since 2014, whereas the rate distributed under the terms and of serious incidents stabilised on the peak value reached in 2016. In 2018, there was an conditions of the Creative Commons increase in the number of serious incidents compared to the mean value observed in the Attribution (CC BY) license (https:// previous decade. creativecommons.org/licenses/by/ According to [5], with more intensive air traffic, the number of reported civil aviation 4.0/). occurrences increases, too. The authors of this publication processed the data obtained from

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the European Coordination Centre for Aviation Incident Reporting Systems (ECCAIRS), which analyses the reliability and safety of large aircrafts in terms of aviation occurrences by individual categories, as defined by the International Civil Aviation Organisation (ICAO). Civil aviation occurrences are rarely a result of a single cause. Janic [6] summarised the causes of civil aviation occurrences as follows: pilot human error, mechanical failures, air traffic control errors, ground support failures, and dangerous weather conditions. Ac- cording to [7], such occurrences are usually caused by various combinations of multiple circumstances. Kharoufah et al. stated that human errors contributed to almost 75% of the aviation accidents and other occurrences [8]. The authors observed that the most important human factor that contributes to aviation accidents and incidents is the situational aware- ness followed by non-adherence to procedures). According to [9], as much as 79% of the fatal accidents which occurred in the USA in 2006 were attributed to a pilot error. Accord- ing to Caldwell [10], the tiredness of pilots also negatively affects the crew’s capabilities, which may significantly contribute to civil aviation occurrences. The impact of managerial and organisational effects (e.g., pilot errors, ATC errors, maintenance staff errors, and technology failures) on the air traffic failures were examined by Lin et al. [11]. According to [12], maintaining operational safety and the status of airport runway (especially in bad weather) is very important for the overall aviation safety. Li et al. [13] analysed 41 civil aviation accidents which happened to the aircraft registered in the Republic of China in the years 1999–2006. They observed that incorrect decisions at higher control levels may indirectly impair the performance of pilots, and this consequently leads to accidents. Incidents represent an important subgroup of civil aviation occurrences. According to [14], although incidents are not paid as much attention as is paid to accidents, it is still important to investigate incidents to identify dangerous conditions that might lead to serious occurrences. The most frequent aviation incident, i.e., a collision of an aircraft with a bird, and a correlation between the type of incidents and changes in the temperature cycle are discussed in the paper [15]. The authors proposed a simulation model for predicting the probability of an aviation incident caused by a collision of an aircraft with a bird. According to [14,16], the absence of the aircraft maintenance causes a more intensive wear and ageing of most system components, and this leads to their complete wear or failure and subsequently disrupts the safety of the system. Marais and Robichaud observed, based on the data from the years 1999–2008, that the accidents associated with maintenance are approximately 6.5 times more likely to be fatal than accidents in general [14]. Insley and Turkoglu [16] examined and analysed aviation accidents and serious incidents associated with the aircraft maintenance that occurred in the years 2003–2017. They observed that the most frequent causes of civil aviation occurrences were runway excursions and air turnbacks, while the second-level categories were associated with failures of engine and landing gear systems. Roelen et al. [17] pointed out a need for the models representing potential scenarios of a succession of causal occurrences, including the technical, human and organisational factors. The authors [18] created a hierarchically structured model containing various accident scenarios in different flight stages. They created the model by applying the methodology combining the event sequence diagrams, fault trees, and Bayesian belief networks. A causal model of air traffic safety, based on a study of accidents and incidents over the last two decades, was described in the paper [19]. The authors created the model by applying the event sequence diagrams, fault trees, and a Bayesian belief network. The paper [20] presents an accident model based on the elementary concepts of the systems theory. According to Leveson, the use of such a model provides the theoretical basis for implementing unique novel types of accident analyses, hazard analyses and accident prevention strategies, including novel approaches to safety designing. Blom and Bloem [21] applied the Bayesian estimation of the function of a combined conditional rate of accidents and statistical data on accidents and flights. A structured process for the creation of a qualitative model of evaluation that might be used by airline companies to identify Sustainability 2021, 13, 5396 3 of 17

human errors and select an intervention strategy with the highest potential for success was described in the paper [22]. Zhang and Mahadevan [23] analysed the accidents of passenger airline companies that happened in the years 1982–2006. They identified the correlations between the causes of accidents by applying the Bayesian network. The paper [24] described the identification of common causes of serious and major incidents in the air traffic by applying the Heinrich’s triangle. According to this theory, the causes identified at high severity levels are always located at low levels. In the analysis, the authors of the paper used the data on serious and major incidents for four consecutive years. Boyd and Howell [25] applied the method of statistical analysis (Poisson distribution, contingency tables, hypothesis testing) in order to analyse the rates of aviation accidents. Mannering and Bhat [26] discussed the methods used in the field of accident analyses (e.g., Poisson regression model, generalised estimating equation models, Poisson and negative binomial regression models, etc.). The effects of the financial factors which influence the maintenance policy, procurement and training in airline companies on air traffic safety are described in the paper [27]. The study monitored 110 airline companies operating in 26 countries, and the analyses and evaluations were carried out while applying, for example, testing methods, Poisson regression, etc. Similarly, the paper [28] described the investigation of the effects of particular business decisions of airline companies on the tendency for aircraft accidents. The author studied the probability of an aviation accident using the Poisson and negative binomial regression models. Li et al. applied the geographically weighted Poisson regression to create crash prediction models at the district level [29]. A spatial regression model was used in the analysis of road traffic accidents, as described in the paper [30]. Salvagioni et al. [31] investigated a potential correlation between teachers’ burnout and car accidents that happened to teachers. The research was carried out with 509 teachers, and one of the accident occurrence evaluation methods was the Poisson regression model. The investigation, identification and evaluation of the factors affecting car accidents were carried out while applying the negative binomial distribution and the Poisson regression methods [32]. Gildea et al. [33] applied the Poisson regression to analyse the use of antihistamines, which may deteriorate the pilot’s performance and hence contribute to an aircraft accident. The present article analyses civil aviation occurrences in Slovakia. A Pareto analysis was used to identify the key categories of civil aviation incidents in Slovakia. A negative trend in the number of civil aviation occurrences is also affected by the development and expansion of air transport in the country. Therefore, the model of correlations between the number of civil aviation occurrences and selected input variables was created while applying the multiple regression analysis and the Poisson regression.

2. Materials and Methods 2.1. Accident Rates in Slovakia Slovakia (Slovak Republic) is an inland country located in Central Europe (Figure1), with a total area of 49,035 km2. Its population is approximately 5.45 million inhabitants, with Bratislava as the capital. Since 2004, it belongs to the European Union. Natural conditions in Slovakia are less favourable to transport development (moun- tainous terrain for road transport; rivers not suitable for water transport; poor railway connections in the southern regions of the SR; insufﬁcient use of local airports, etc.). One of the key problems in the transport sector in Slovakia is a prolonged negative trend in the distribution of transportation jobs in favour of the road transport, in particular the individual (non-public) transport [34]. In 2018, the total length of the state-managed road network was 18,059 km. As much as 57.4% of the total road network represented Class III roads (10,358 km). Only 4.3% of the road network represented highways and expressways. Sustainability 2021, 13, 5396 4 of 17 Sustainability 2021, 13, x FOR PEER REVIEW 4 of 18

FigureFigure 1. 1.Slovakia Slovakia and and neighbouring neighbouring countries. countries.

ClassOne Iof roads the key and problems Class II roads in the represented transport se 18.3%ctor andin Slovakia 20.0% (accordingly) is a prolonged of thenegative total lengthtrend in of the the distribution road network. of transportation In 2018, 3580 jobs km in of favour railways of the were road operated. transport, Over in particular the last 5the years, individual there was (non-public) a slight upward transport trend [34]. in the In performance2018, the total of thelength rail of passenger the state-managed transport. roadIn network Slovakia, was there 18,059 are km. 30 active As much airports, as 57 including.4% of the 14 total civil road public network airports, represented 13 civil non-publicClass III roads airports (10,358 and 3km). military Only airports. 4.3% of Outthe road of the network total number represented of civil airports,highways only and 4expressways. airports perform regular transportation. In addition to the above-stated number, there are alsoClass 9 heliports I roads and and Class approximately II roads represented 60 airports 18.3% for agricultural, and 20.0% forestry(accordingly) and water of the managementtotal length of aviation the road [35 network.]. In 2018, 3580 km of railways were operated. Over the last 5 years,Water there transport was a slight is carried upward out trend primarily in the on performance the Danube of River, the rail and passenger partially transport. also on the VáInh River,Slovakia, while there the lengthare 30 ofactive all navigable airports, linesincluding is only 14 172 civil km. public The Danube airports, River, 13 civil as anon-public waterway airports of international and 3 military importance, airports. should Out of provide the total (according number of to civil the international airports, only classification4 airports perform of inland regular waterways) transportation. a certain transport In addition capacity, to the determined above-stated as min.number, 300 daysthere perare year. also However,9 heliports an and analysis approximately indicated that 60 waterairports transport for agricultural, experiences forestry certain and problems water withmanagement the waterway aviation infrastructure. [35]. Therefore, a comprehensive review of transport accident rates inWater Slovakia transport does notis carried include out water primarily transport. on the Danube River, and partially also on the VáhA road River, traffic while accident the length is an occurrenceof all naviga causedble lines as a is result only of172 a movingkm. The vehicle Danube in River, road trafficas a waterway which results of international in a fatality, importance, injury or damage should provide to property, (according regardless to the of international whether it isclassification classified as of a crimeinland or waterways) an offence, a andcertain whether transport it is resolvedcapacity, bydetermined a court or as the min. penal 300 commissiondays per year. of the However, traffic inspectorate. an analysis Aindicated rail accident that iswater an accident transport involving experiences at least certain one movingproblems rail with vehicle. the Rail waterway accidents infrastructure. include, for example, Therefore, collisions, a comprehensive derailments, accidentsreview of attransport railway crossings,accident rates accidents in Slovakia of persons does causednot include by a movingwater transport. railway car, fires in railway fleets,A etc. road traffic accident is an occurrence caused as a result of a moving vehicle in road trafficAn which aviation results accident in a fatality, is an occurrence injury or damage associated to property, with the regardless operation of of whether an aircraft it is which,classified in the as casea crime of a or manned an offence, aircraft, and takes whethe placer itbetween is resolved the by time a court any person or the boardspenal com- the aircraft with the intention of flight until such time as all such persons have disembarked [36]. mission of the traffic inspectorate. A rail accident is an accident involving at least one During such a period, a person involved may be fatally or seriously injured as a result of moving rail vehicle. Rail accidents include, for example, collisions, derailments, accidents being in the aircraft or in direct contact with any part of the aircraft, or if the aircraft sustains at railway crossings, accidents of persons caused by a moving railway car, fires in railway damage or structural failure, or if an emergency occurs due to the aircraft disappearing fleets, etc. from the radars. An aviation accident is an occurrence associated with the operation of an aircraft The data obtained from the Ministry of Transport of the Slovak Republic indicated which, in the case of a manned aircraft, takes place between the time any person boards that in the period from 2009 to 2019 there were 173,322 accidents altogether in the road, the aircraft with the intention of flight until such time as all such persons have disem- railway and air transport in Slovakia [2]. Basic descriptive characteristics of the number barked [36]. During such a period, a person involved may be fatally or seriously injured of accidents in Slovakia are presented in Table1. A graphical representation of traffic as a result of being in the aircraft or in direct contact with any part of the aircraft, or if the accidents in Slovakia which occurred in the period from 2009 to 2019 is shown in Figure2. aircraft sustains damage or structural failure, or if an emergency occurs due to the aircraft disappearing from the radars. The data obtained from the Ministry of Transport of the Slovak Republic indicated that in the period from 2009 to 2019 there were 173,322 accidents altogether in the road, railway and air transport in Slovakia [2]. Basic descriptive characteristics of the number Sustainability 2021, 13, x FOR PEER REVIEW 5 of 18

of accidents in Slovakia are presented in Table 1. A graphical representation of traffic accidents in Slovakia which occurred in the period from 2009 to 2019 is shown in Figure 2.

Sustainability 2021, 13, 5396 Table 1. Descriptive statistics of accident rates in Slovakia in the period of 2009–2019. 5 of 17 Transport Characteristics Air Road Railway NumberTable for 1. Descriptivethe entire period statistics of accident 150 rates in Slovakia 172,173 in the period of 2009–2019. 999 Maximum value 26 25,989 190 Transport MinimumCharacteristics value 6 13,307 60 Average number per year 13.64 Air 15,652.09 Road 90.82 Railway StandardNumber deviation for the entire period 6.772 150 4169.01 172,173 36.989 999 Maximum value 26 25,989 190 Minimum value 6 13,307 60 As much as 99.2% of all accidents were accidents in road transport. Aviation acci- Average number per year 13.64 15,652.09 90.82 dents representedStandard a negligible deviation portion of the to 6.772tal accident rate. 4169.01 Over the last 11 36.989years, only 0.1% of the total number of traffic accidents in Slovakia were aviation accidents.

FigureFigure 2. Review 2. Review of traffic of trafﬁcaccide accidentsnts in Slovakia in Slovakia (2009–2019). (2009–2019).

The basicAs much numerical as 99.2% characteristics of all accidents of the were numb accidentser of fatal in road or serious transport. injuries Aviation in traffic accidents accidentsrepresented in Slovakia a negligible are listed portion in Table of 2. the total accident rate. Over the last 11 years, only 0.1% of the total number of trafﬁc accidents in Slovakia were aviation accidents. Table 2. Descriptive statisticsThe of basicthe number numerical of fatal characteristics or serious injuries of the for numberthe period of of fatal 2009–2019. or serious injuries in trafﬁc accidents in Slovakia are listed in Table2. Number of Injuries in Traffic Accidents CharacteristicsTable 2. Descriptive statisticsAir Transport of the number of fatal or Road serious Transport injuries for the period Railway of 2009–2019. Transport

Fatal Serious NumberFatal of InjuriesSerious in Trafﬁc AccidentsFatal Serious Number for the entire period 29 37 3034 12,716 550 411 Characteristics Air Transport Road Transport Railway Transport Maximum value 7 Fatal 7 Serious 347 Fatal 1408 Serious 78 Fatal 45 Serious Minimum value 0 0 223 1050 26 33 Number for the entire period 29 37 3034 12,716 550 411 Average numberMaximum per value year 2.64 7 3.36 7 275.82 347 1156 1408 50 78 37.36 45 StandardMinimum deviation value 2.06 0 2.34 045.40 223 105.94 1050 19.42 263.83 33 Average number per year 2.64 3.36 275.82 1156 50 37.36 Standard deviationThe number 2.06 of fatal injuries 2.34 represents 45.40 the number 105.94 of fatalities 19.42 among the crews 3.83 (crews of the relevant means of transport), passengers and third parties that occurred in accidents. AThe serious number injury of is fatal an injury injuries experien representsced by the a person number in ofan fatalitiesaccident that among requires the crews hospitalisation(crews of thefor relevantmore than means 48 h, of commenci transport),ng passengerswithin 7 days and from third the parties date thatthe occurredinjury in was received,accidents. or A which serious results injury in is a anfracture injury of experienced any bone, or by an a personinjury to in any an accident internal thatorgan, requires hospitalisation for more than 48 h, commencing within 7 days from the date the injury was received, or which results in a fracture of any bone, or an injury to any internal organ, etc. A graphical representation of the number of fatal injuries and the number of serious injuries in trafﬁc accidents in Slovakia is shown in Figure3. Sustainability 2021, 13, x FOR PEER REVIEW 6 of 18

Sustainability 2021, 13, 5396 6 of 17 etc. A graphical representation of the number of fatal injuries and the number of serious injuries in traffic accidents in Slovakia is shown in Figure 3.

FigureFigure 3. 3. AA comparison comparison of of the the numbers numbers of of fatal fatal and and serious serious injuries injuries in in traffic traffic accidents. accidents. Within the monitored period, 3613 people died in traffic accidents (83.98% in road Within the monitored period, 3613 people died in traffic accidents (83.98% in road transport; 15.22% in railway transport; and 0.80% in civil aviation). As much as 13,164 peo- transport; 15.22% in railway transport; and 0.80% in civil aviation). As much as 13,164 ple suffered serious injuries in traffic accidents (96.60% in road transport; 3.12% in railway people suffered serious injuries in traffic accidents (96.60% in road transport; 3.12% in transport; and 0.28% in civil aviation). railway transport; and 0.28% in civil aviation). 2.2. Civil Aviation Occurrences 2.2. Civil Aviation Occurrences According to Regulation L13 [2], a civil aviation occurrence (CAO) is a general term for occurrencesAccording associated to Regulation with the L13 operation [2], a civil of av aniation aircraft occurrence that affect (CAO) or could is a affect general air trafficterm forsafety, occurrences and whose associated consequences with the are operation assessed as of an an aviation aircraft accident,that affect a seriousor could incident, affect air an trafficincident safety, or a and ground whose incident. consequences are assessed as an aviation accident, a serious incident,A an serious incident incident or a ground is an incident incident. with a high probability of an accident. It is an occur- renceA likelyserious to incident develop is into an incident an aviation with accident. a high probability A serious incident of an accident. includes, It is for an example, occur- rencea near likely collision, to develop hazardous into an proximity, aviation accident. landing A on serious and takeoff incident from includes, an engaged for example, runway, afires near and collision, smoke hazardous in the passenger proximity, compartment, landing on etc. and Examples takeoff of from other an serious engaged incidents runway, are firespresented and smoke in Annex in the C passenger to the L13 compartment, publication of etc. the AeronauticalExamples of other Information serious Servicesincidents of arethe presented Slovak Republic. in Annex Aviation C to the occurrences L13 publicatio aren always of the Aeronautical classified by aInformation competent authorityServices ofthat the isSlovak authorised Republic. to investigate Aviation occurrences the causes of are civil always aviation classified accidents by a and competent incidents author- [2]. ity thatAn is authorised aviation incident to investigate is an occurrence the causes otherof civil than aviation an accident accidents associated and incidents with [2]. the operationAn aviation of an aircraftincident that is an affects occurrence or could other affect than the an safety accident of operation. associated It consistswith the in op- the erationmisconduct of an ofaircraft a person that or affects an improper or could operation affect the of safety civil aviationof operation. and ground It consists equipment in the misconductin air traffic, of ora person management or an improper and organisation operation thereof, of civil withaviation consequences and ground which equipment do not inusually air traffic, require or management the early termination and organisation of the flightthereof, or with the execution consequences of non-standard which do not or usuallyemergency require procedures the early [2 termination]. The causes of of the incidents flight or also the include execution natural of non-standard phenomena (e.g., or emergencya bird strike, procedures a static electricity [2]. The causes discharge, of inci etc.)dents with also consequences include natural that phenomena do not jeopardise (e.g., aflight bird strike, safety toa static the extent electric thatitya discharge, serious incident etc.) with or an conseq aviationuences accident that do occurs. not jeopardise According flightto Regulation safety to the L13, extent aviation that incidentsa serious inci aredent categorised or an aviation according accident to their occurs. causes According as flight toincidents, Regulation technical L13, aviation incidents, incidents causes associatedare categorised with air according traffic control, to their support causes technology, as flight incidents,etc. In the technical disputable incidents, cases, causes decisions associated on classifying with air an traffic incident control, as asupport serious technol- incident ogy,are etc. made In bythe thedisputable head of cases, the team, decisions who consultson classifying with thean incident director as of a the serious Civil incident Aviation areAuthority, made by if the necessary. head of the team, who consults with the director of the Civil Aviation Authority,A ground if necessary. incident is an incident that occurs outside the period defined in the Regu- lation L-13 [2] and which is associated with the aircraft preparation for the flight, aircraft attendance, servicing, maintenance or repairs or standby, and which results in an injury or fatality or in aircraft damage or destruction. Sustainability 2021, 13, 5396 7 of 17

A more comprehensive evaluation of civil aviation occurrences in Slovakia was carried out using the data on the number of civil aviation accidents, serious incidents, incidents and ground incidents that occurred in the monitored period. A list of 18 incident categories that were monitored and analysed for civil aviation occurrences is presented in Table3.

Table 3. Selected incidents in civil aviation according to [3,37].

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 Occurrences involving collisions/near I3 I12 Declared Incerfa, Alerfa, Detresfa collisions with bird(s)/wildlife I4 Safety landing I13 Occurrences involving ATM or ATS I5 Emergency landing I14 Laser Loss of aircraft control while the aircraft is on the I6 Loss of separation I15 ground STCA, ACAS, MSAW, APW, GPWS, I7 I16 Miscellaneous occurrences in the passenger cabin A-SMGCS ACFT deviation from the ATM approval or I8 I17 Medical emergency from the planned ATC procedures I9 Runway Incursion I18 Illegal radio broadcasting Notes: Short Term Conflict Alert (STCA), Airborne Collision Avoidance System (ACAS), Minimum Safe Altitude Warning (MSAW), Area Proximity Warning (APW), Ground Proximity Warning System (GPWS), Advanced Surface Movement Guidance & Control System (A-SMGCS), Army Combat Fitness Test (ACFT), Air Traffic Management (ATM), Air Traffic Control (ATC), Air Traffic Services (ATS).

The uncertainty phase (Incerfa) is a situation wherein uncertainty exists as to the safety of an aircraft and its occupants. Alert phase (Alerfa) is a situation wherein apprehension exists as to the safety of an aircraft and its occupants. Distress phase (Detresfa) is a situation wherein there is a reasonable certainty that an aircraft and its occupants are threatened by grave and imminent danger and require immediate assistance [38]. For a more comprehensive assessment of the CAO rates, the following additional parameters were determined: millions of passengers transported in Slovakia in a given year; the amount of transported goods (thousands of tonnes) in a monitored year; the number of civil planes in the Register of SR (in pieces); the number of commercial aircraft (in pieces); the number of commercial aircraft aged above 14 years in a given year (in pieces); and the number of total aircraft movements (in thousands) in a given year. The total aircraft movements include landings and takeoffs of aircrafts to/from airports. The analysis was carried out using the data obtained from the sources published by the Ministry of Transport of the Slovak Republic [37] and from the Eurostat [39] and STATdat databases [40].

2.3. Statistical Methods The analysis of the current situation regarding CAOs in Slovakia was carried out by applying basic statistical methods (descriptive statistics and hypothesis testing), a Pareto analysis, a classical multiple regression model and a Poisson regression model. All data were evaluated, and the results were obtained using the R package software.

2.3.1. Hypothesis Testing Statistical hypotheses were tested using a p-value, based on the principle that if the p-value is lower than the determined signiﬁcance level α, then the null hypothesis is rejected in favour of the alternative hypothesis. If the p-value is higher than the determined signiﬁcance level α, then the null hypothesis is not rejected.

2.3.2. Pareto Analysis The Pareto analysis is an important decision-making tool, as it facilitates the determination of priorities when solving a problem. The purpose of the Pareto analysis was Sustainability 2021, 13, 5396 8 of 17

to separate important factors, causes of a certain problem, from those less important, and show where our efforts should be primarily directed to improve the process. The Pareto analysis uses the 80/20 rule, i.e., a more detailed analysis of causes should be carried out with a cumulative frequency from 0 to 80%, or from 0 to 75%. A graphical tool of the Pareto analysis is a Pareto diagram. The Pareto diagram is a bar chart of absolute or absolute relative frequencies of the occurrence of individual causes; it also contains the Lorentz curve representing the polygon of cumulative relative frequencies of the occurrence of individual causes (in %) [41].

2.3.3. Multiple Linear Regression The correlations between a dependent variable and several input variables were described and modelled by applying a regression analysis. We assumed that the correlation between the dependent variable Y and k-explanatory variables Xi, i = 1, ... , k was expressed by the following model:

k Y = β0 + ∑ βiXi + ε, (1) i=1

where β0 and βi for i = 1, ... , k are the regression model coefficients and ε is the random error. The model coefficients were identified by applying the method of least squares. The statistical significance of the regression model was determined by the t-test of statistical significance of the model. A degree of the correlation between variable Y and k-explanatory variables was expressed by the coefficient of multiple determination r2. The coefficient values ranged within the interval h0;1i. As the value approached 1, the correlation was stronger.

2.3.4. Poisson Regression Model The Poisson regression model was a basic model used for modelling the number of occurrences, and the general linear regression model was used for modelling real continuous data. According to [42], it is a special type of the generalised linear model. The application of the Poisson regression model was based on the assumption that a random parameter Y exhibited the Poisson distribution. Let Xi, i = 1, ... , k be the k-independent variables. The equation of the Poisson model, which considers all input variables, is generally as follows:

k ln(Y) = β0 + ∑ βiXi (2) i=1

where β0 and βi for i = 1, ... , k are the model coefﬁcients. Sometimes, a modiﬁed form of the model is used:

+ k X k X X X X X X Y = eβ0 ∑i=1 βi i = eβ0 e∑i=1 βi i = eβ0 eβ1 1 eβ2 2 eβ3 3 eβ4 4 ... eβk k (3)

The model coefficients were estimated by applying the maximum likelihood method for the regression model. In Model (2), coefficient βi represented an expected change in β the ln of the variable Y per unit change in the input variable Xi. Coefficient e i in Model (3) represented a multiplicative effect on the variable Y if the ith—variable Xi changes by one unit, with the remaining variables unchanged. A positive value of coefficient βi means that as the value of variable Xi increases by 1 (with the remaining variables unchanged), the monitored output variable Y increases too. A negative value of coefficient βi indicates that if the Xi value increases by 1 (with the remaining variables unchanged), the output variable Y decreases. The Poisson regression does not allow for a calculation of the coefficient of determination r2, 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 Sustainability 2021, 13, x FOR PEER REVIEW 9 of 18

one unit, with the remaining variables unchanged. A positive value of coefficient 𝛽 means that as the value of variable 𝑋 increases by 1 (with the remaining variables unchanged), the monitored output variable Y increases too. A negative value of coefficient 𝛽 indicates that if the 𝑋 value increases by 1 (with the remaining variables unchanged), the output variable Y decreases. The Poisson regression does not allow for a calculation of the coefficient of determi- Sustainability 2021, 13, 5396 9 of 17 nation r2, 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 R2 for Poisson regression, which may be interpreted similarly to r2 [43]. All data werepseudo evaluated, R2 for Poissonand the regression,results were which obtained may using be interpreted the R package similarly software to r2 [44].[43]. All data were evaluated, and the results were obtained using the R package software [44]. 3. Results and Discussion 3. Results and Discussion The investigation was carried out with the aim of: The investigation was carried out with the aim of: • Analysing civil aviation occurrences for the period from 2000 to 2019; • • DeterminingAnalysing civil the key aviation categories occurrences of incidents for the that period largely from affect 2000 the to 2019;occurrence of inci- • dentsDetermining in civil aviation; the key categories of incidents that largely affect the occurrence of • Modellingincidents a in correlation civil aviation; between the civil aviation occurrences (CAOs) and selected • inputModelling variables a correlation by applying between the mu theltiple civil and aviation Poisson occurrences regressions. (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 3.1. Analysis of Civil Aviation Occurrences for the Period from 2000 to 2019 The number of CAOs in Slovakia that occurred in the period from 2000 to 2019 is The number of CAOs in Slovakia that occurred in the period from 2000 to 2019 is graphicallygraphically represented represented in in Figure Figure 44.. The chartchart indicatesindicates that that the the number number of of CAOs CAOs exhibited exhib- itedan an upward upward trend trend before before 2012 2012 and and reached reache thed the peak peak value value in in 2012, 2012, when when the the number number of ofCAOs CAOs waswas 453.453. InIn the years 2013–2017, th thee CAO CAO development development was was almost almost constant, constant, and and sincesince 2017 2017 the the number number of of CA CAOsOs has has been been rising rising again. again.

Figure 4. Civil aviation occurrences (period 2000–2019). Figure 4. Civil aviation occurrences (period 2000–2019). The development of civil aviation accidents in the period from 2000 to 2019 is shown The development of civil aviation accidents in the period from 2000 to 2019 is shown in Figure5. In 2004, the number of civil aviation accidents reached the maximum value in Figure 5. In 2004, the number of civil aviation accidents reached the maximum value in in the monitored period, i.e., 30 accidents. The average annual number of civil aviation the monitored period, i.e., 30 accidents. The average annual number of civil aviation acci- accidents for the monitored period was 17. dents for the monitored period was 17. The number of fatal and serious injuries in civil aviation accidents for the period from 2000 to 2019 is shown in Figure5. The highest number of fatal injuries was observed in 2006 when 42 Slovak soldiers of KFOR peacekeeping forces died in an accident of the Slovak Air Force aircraft. The percentages of individual CAO types in the total number of CAOs are listed in Table4. The data analysis published by the Ministry of Transport indicated that since 2003 incidents represent the highest percentage in all CAOs. The percentages of aviation accidents, serious incidents, incidents and ground incidents in of the total number of CAOs are listed in Table4. SustainabilitySustainability 20212021,, 1313,, x 5396 FOR PEER REVIEW 1010 of of 18 17

FigureFigure 5. 5. AviationAviation accidents, accidents, the the number number of offatalities fatalities and and injuries injuries in civil in civil aviation aviation accidents accidents (period (pe- 2000–2019).riod 2000–2019).

Table 4. TheList number of CAOs of fatal and theirand serious percentages injuries in the in total civil number aviation of CAOsaccidents [%]. for the period from 2000Year to 2019 AAis shown SI in Figure I 5. The GIhighest Yearnumber of AA fatal injuries SI was I observed GI in 2006 when 42 Slovak soldiers of KFOR peacekeeping forces died in an accident of the 2000 36.4 34.1 9.1 20.5 2010 6.3 0.5 60.5 32.8 Slovak2001 Air Force 35.0 aircraft. 35.0 22.5 7.5 2011 4.6 0.8 66.4 28.2 2002The percentages 29.1 23.6of individual 36.4 CAO 10.9 types 2012in the total 4.4 number 1.1 of CAOs 56.9 are listed 37.5 in Table2003 4. The 27.3data analysis 17.0 published 52.3 by the 3.4 Ministry 2013 of Transport 4.2 indicated 3.4 89.3that since 3.1 2003 incidents2004 represent 27.0 the 21.6 highest 51.4 percentage 0.0 in all 2014 CAOs. The 2.6 percentages 0.7 of 95.6 aviation 1.1acci- dents,2005 serious 7.1 incidents, 4.0 incidents 84.8 and 4.0ground 2015incidents 2.5in of the 1.1total number 96.1 of CAOs 0.3 are2006 listed in 10.2Table 4. 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 Table 4. List2009 of CAOs 6.1 and their 2.2 percentages 56.5 in the 35.1 total number 2019 of CAOs 3.3 [%]. 0.0 94.2 2.5 Year AA SINotes: Aviation I accidents (AA), GI serious incidents Year (SI), incidentsAA (I), ground SI incidents (GI). 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 The data22.5 show that 7.5 the percentage 2011 of civil4.6 aviation accidents 0.8 in 66.4 the total number28.2 of CAOs has been decreasing since 2005. Since that year, the number of serious incidents 2002 29.1 23.6 36.4 10.9 2012 4.4 1.1 56.9 37.5 dramatically decreased; in 2005, the number of serious incidents decreased by almost 62% 2003 27.3 17.0 52.3 3.4 2013 4.2 3.4 89.3 3.1 compared to the previous year, 2004. Since 2005, the average number of serious incidents 2004 27.0 21.6 51.4 0.0 2014 2.6 0.7 95.6 1.1 was 7. A graphical representation of the number of serious incidents, incidents and ground 2005 7.1 4.0incidents 84.8 in civil aviation4.0 in Slovakia2015 for the period2.5 from 2000 1.1 to 201996.1 is shown in Figure 0.3 6. 2006 10.2 3.6 While83.2 the number3.0 of serious2016 incidents has3.6 decreased 0.7 since 2004,95.7 the number0.0 of inci- 2007 10.6 1.0dents has79.8 dramatically 8.6 increased 2017 since 2005 (Figure4.2 6, Table 0.84). Similarly,93.8 their percentage1.2 2008 8.2 4.1in the total 65.3 number of22.4 CAOs has2018 increased too.1.7 In 2015, incidents 0.0 represented94.8 the 3.5 highest 2009 6.1 2.2percentage 56.5 of all CAOs35.1 (as much2019 as 96%, i.e.,3.3 as much as 0.0 259 incidents94.2 out of the 2.5 total Notes: Aviationnumber accidents of 271 (AA), CAOs serious in thatincidents year, (SI), Table incidents4). The (I), same ground trend incidents of a high (GI). number of incidents was observed in the following years. A negative upward trend in the number of incidents is largelyThe data associated show that with the air percentage traffic intensity, of civil which aviation increases accidents year byin year,the total and number hence with of CAOsthe denser has been air space decreasing above thesince Slovak 2005. Republic. Since that year, the number of serious incidents dramaticallySince 2013, decreased; there was in 2005, also athe significant number of decrease serious inincidents the number decreased of ground by almost incidents. 62% comparedThe average to the percentage previous inyear, the 2004. period Since from 200 20135, the to average 2019 was number 1.7% of serious the total incidents number wasof CAOs. 7. A graphical representation of the number of serious incidents, incidents and groundA comparisonincidents in ofcivil two aviation years, 2000in Slovakia and 2019, for showedthe period significant from 2000 changes to 2019 in is the shown number in Figureof CAOs. 6. The number of CAOs in 2019 was 8.2 times higher than that in 2000. The highest increase, when compared to 2000, was observed in the number of incidents (84.5 times more than in 2000). Sustainability 2021, 13, 5396 11 of 17

The increased number of CAOs is related to the increase of air transport in Slovakia. While in 2000 there were almost 0.43 mil. passengers, in 2005 there were more than 1.6 mil. passengers (an increase of around 270% compared with 2000). In 2010, there were more Sustainability 2021, 13, x FOR PEER REVIEW 11 of 18 than 1.97 mil. passengers (an increase of about 23% compared with 2005) and in 2018 there were almost 2.97 mil. passengers (an increase of around 50% compared with 2010).

FigureFigure 6. 6. SSeriouserious incidents, incidents, incidents incidents and and ground ground incidents incidents (period (period 2000–2019). 2000–2019). 3.2. Determination of the Key Categories of Civil Aviation Incidents in Slovakia While the number of serious incidents has decreased since 2004, the number of incidents Thehas dramatically number of incidents increased has since been 2005 rising (Fig sinceure 6, 2009,Table which4). Similarly, represents their a percentage signiﬁcant inportion the total of thenumber total numberof CAOs of has CAOs. increased The analysis too. In of2015, the causesincidents of incidentsrepresented in civil the aviationhighest was carried out with 18 incident categories (Table5), as published in the reports on CAOs percentage of all CAOs (as much as 96%, i.e., as much as 259 incidents out of the total for the period from 2009 to 2018. A review of individual incident categories is shown in number of 271 CAOs in that year, Table 4). The same trend of a high number of incidents Figure7. was observed in the following years. A negative upward trend in the number of incidents is largely associated with air traffic intensity, which increases year by year, and hence with Table 5. Descriptive statistics of the number of incidents for the period 2009–2018. the denser air space above the Slovak Republic. Since 2013, there was also a significantIncident decr Categoryease in [Number] the number of ground incidents. Characteristics The average percentageI1 I2in the period I3 from I4 2013 to I5 2019 was I6 1.7% of I7 the total I8 number I9 of Number for the whole periodCAOs. 267 57 607 19 19 61 96 191 13 Maximum valueA comparison 44 of two 13 years, 2000 78 and 2019, 7 showed 5 significant 14 changes 45 in 46 the number 5 Minimum valueof CAOs. The number 11 of 1CAOs in 35 2019 was 0 8.2 times 0 higher 0 than that 2 in 2000. 9 The highest 0 Average number per yearincrease, when 26.70 compared 5.70 to 2000, 60.70 was observ 2.38ed 2.38 in the number 6.10 of 9.60 incidents 19.1 (84.5 2.17times Standard deviation 10.10 3.80 12.91 2.45 1.85 3.70 13.01 10.79 1.72 more than in 2000). Percentage for the monitored periodThe [%] increased 12.19 number 2.60 of CAOs 27.72 is related 0.87 to 0.87the increase 2.79 of air 4.38 transport 8.72 in Slovakia. 0.59 CharacteristicsWhile in 2000 there I10 were I11 almost I12 0.43 mil. I13 passengers, I14 in I152005 there I16 were more I17 than I18 1.6 Number for the whole periodmil. passengers 197 (an increase 343 of around 50 270% 3 compared 237 with 13 2000). 5 In 2010, 9 there were 3 Maximum valuemore than 1.97 mil. 44 passengers 60 (an 22 increase 2 of about 37 23% compared 4 with 2 2005) 3 and in 2018 2 Minimum valuethere were almost 7 2.97 mil. 20 passengers 1 (an 0 increase 22 of around 1 50% compared 0 1 with 2010). 0 Average number per year 28.14 38.11 5.56 0.50 29.63 2.60 0.83 1.80 0.60 Standard deviation3.2. Determination 11.91 of the 10.79Key Categories 6.67 of Civil 0.84 Aviation 5.95 Incidents 1.14 in Slovakia 0.75 0.84 0.89 Percentage for the monitored periodThe [%] number 9.00 of incidents 15.67 has 2.28 been rising 0.14 since 10.82 2009, 0.59which represents 0.23 0.41 a significant 0.14 portion of the total number of CAOs. The analysis of the causes of incidents in civil aviation was carried out with 18 incident categories (Table 5), as published in the reports on CAOs for the period from 2009 to 2018. A review of individual incident categories is shown in Figure 7. SustainabilitySustainability 20212021, 13, 13, x, 5396FOR PEER REVIEW 1212 of of 18 17

Figure 7. Review of incident categories in the years 2009 through 2018. Figure 7. Review of incident categories in the years 2009 through 2018. The highest number of incidents was observed in the following categories: I3 (occur- The highest number of incidents was observed in the following categories: I3 (occurrences involving collisions/near collisions with bird(s)/wildlife), I11 (failure or malfunction rences involving collisions/near collisions with bird(s)/wildlife), I11 (failure or malfunc- of an aircraft system), I1 (loss of communication during the flight), I14 (laser) and I10 (unau- tionthorised of an aircraft penetration system), of air I1 space).(loss of Thecommunication characteristics during of individual the flight), incidents I14 (laser) (number and I10 of (unauthorisedincidents for thepenetration monitored of period,air space). average The annualcharacteristics number, of standard individual deviation, incidents maximum (num- berand of minimumincidents numberfor the monitored of incidents) period, are shown average in Tableannual5. number, standard deviation, maximum2190 and incidents minimum of the number monitored of incidents) categories are shown occurred in duringTable 5. the whole monitored period. The highest percentage was observed in Category I3 (occurrences involving colli- Table 5. Descriptive statistics of the number of incidents for the period 2009–2018. sions/near collisions with bird(s)/wildlife; 27.72%) and Category I11 (failure or malfunction of an aircraft system; 15.67%).Incident Almost 12.19%Category of [Number] the incidents belong to Category Characteristics I1 (loss of communicationI1 I2 during I3 the flight)I4 and 10.82%I5 toI6 Category I7 I14 (laser).I8 TheI9 per- Number for the whole periodcentages of individual 267 categories 57 607 in the total 19 number 19 of incidents 61 96 that occurred 191 in13 the monitored period are shown in Table5. Maximum value 44 13 78 7 5 14 45 46 5 The Pareto analysis was carried out while applying the 75/25 rule, under which it Minimum value 11 1 35 0 0 0 2 9 0 is recommended to analyse in more detail the causes of defects that exhibit a cumulative Average number per year 26.70 5.70 60.70 2.38 2.38 6.10 9.60 19.1 2.17 relative frequency of 75%. The Pareto analysis indicated (Figure8) that almost 76% of the Standard deviationcauses of all incidents 10.10 out3.80 of all CAOs12.91 were2.45 only in 1.85 5 categories: 3.70 I313.01 (occurrences 10.79 involving1.72 Percentage for the monitoredcollisions/near period [%] 12.19collisions 2.60 with bird(s)/wildlife); 27.72 0.87 I11 0.87 (failure 2.79 or malfunction 4.38 8.72 of an aircraft 0.59 Characteristics system); I1 (lossI10 of communication I11 I12 during I13 the flight);I14 I14I15 (laser); andI16 I10 (unauthorisedI17 I18 Number for the whole periodpenetration of air 197 space). 343These categories 50 represent 3 237 the few 13 vital causes 5 that 9 contribute 3 to Maximum value the occurrence of 44 incidents 60 in civil22 aviation 2in Slovakia. 37 4 2 3 2 Minimum value 7 20 1 0 22 1 0 1 0 3.3. Modelling the Number of CAOs Depending on Selected Parameters Average number per year 28.14 38.11 5.56 0.50 29.63 2.60 0.83 1.80 0.60 Standard deviation A negative 11.91 trend in10.79 the number 6.67 of civil 0.84 aviation 5.95 occurrences 1.14 0.75 is affected 0.84 by multiple0.89 factors. In the present investigation, the factors which were taken into consideration Percentage for the monitored period [%] 9.00 15.67 2.28 0.14 10.82 0.59 0.23 0.41 0.14 included the millions of passengers transported in Slovakia, the amount of the transported goods (thousands of tonnes), the number of commercial aircrafts aged above 14 years and 2190 incidents of the monitored categories occurred during the whole monitored pe- the total aircraft movements in a given year (in thousands). riod. The highest percentage was observed in Category I3 (occurrences involving colli- The output count variable Y represents the number of CAOs per year. We assumed sions/near collisions with bird(s)/wildlife; 27.72%) and Category I11 (failure or malfunc- that the investigated variable exhibited the Poisson distribution. The modelling of the tion of an aircraft system; 15.67%). Almost 12.19% of the incidents belong to Category I1 number of CAOs was carried out using seven input (independent) variables, as described (loss of communication during the flight) and 10.82% to Category I14 (laser). The percent- in Table6. The data for all variables are related to the period of 10 consecutive years. ages of individual categories in the total number of incidents that occurred in the monitored period are shown in Table 5. The Pareto analysis was carried out while applying the 75/25 rule, under which it is recommended to analyse in more detail the causes of defects that exhibit a cumulative Sustainability 2021, 13, x FOR PEER REVIEW 13 of 18

relative frequency of 75%. The Pareto analysis indicated (Figure 8) that almost 76% of the causes of all incidents out of all CAOs were only in 5 categories: I3 (occurrences involving collisions/near collisions with bird(s)/wildlife); I11 (failure or malfunction of an aircraft system); I1 (loss of communication during the flight); I14 (laser); and I10 (unauthorised Sustainability 2021, 13, 5396 13 of 17 penetration of air space). These categories represent the few vital causes that contribute to the occurrence of incidents in civil aviation in Slovakia.

FigureFigure 8. 8. ParetoPareto diagram. diagram.

Table 6. Characteristics of the variables. 3.3. Modelling the Number of CAOs Depending on Selected Parameters Variables DescriptionA negative trend in the number of civil aviation occurrences is affected by multiple Dependent Variables factors. In the present investigation, the factors which were taken into consideration in- CAO (Y) Numbercluded of CAOs the inmillions a given of year passengers transported in Slovakia, the amount of the transported Independent Variables goods (thousands of tonnes), the number of commercial aircrafts aged above 14 years and Year (X1) Time variable,the total Year aircraft = 1 for movements year 2009, ..., in Year a given = 10 year for year (in 2018thousands). Passenger (X2) Number ofThe passengers output transported count variable in Slovakia Y represents in a given the year number (in mil.) of CAOs per year. We assumed Goods (X ) Amount of transported goods in a given year (in thousands of tonnes) 3 that the investigated variable exhibited the Poisson distribution. The modelling of the Civil Planes (X4) Number of all civil planes registered in Slovakia in a given year Aircraft (X5) Numbernumber of commercial of CAOs aircraft was carried with the out weight using of seven 9000 kg input and more (independent) in a given year variables, as described Age (X6) Numberin ofTable commercial 6. The data aircraft for with all variables the weight are of 9000 related kg and to morethe period and aged of over10 consecutive 14 years in a years. given year Movement (X7) Number of landings or takeoffs at airports in a given year (in thousands) Table 6. Characteristics of the variables. Variables Description3.3.1. Classical Regression Model (Model I) Dependent Variables The investigation of the impact of selected input variables on the number of CAOs CAO (Y) Numberwas based of CAOs on the in followinga given year model:

Independent Variables 7 Year (X1) Time variable, Year = 1 for year 2009, ...,Y Year= β0 =+ 10∑ forβi Xyeari, 2018 (4) Passenger (X2) Number of passengers transported in Slovakia ini= a1 given year (in mil.) Goods (X3) Amount of transported goods in a given year (in thousands of tonnes) where β0, βi, i = 1, 2, ... , 7 are the coefficients of the regression model. Output variable Civil Planes (X4) NumberY represents of all civil the planes total number registered of in civil Slovakia aviation in occurrencesa given year in a given year. The result Aircraft (X5) Number of commercial aircraft with the weight of 9000 kg and more in a given year of testing indicated that only two variables, X4 (Civil Planes) and X7 (Movement), had Age (X6) Numberstatistically of commercial significant aircraft effects with on the the number weight of of CAOs. 9000 kg The and equation more and of the aged best over regression 14 yearsmodel in a isgiven as follows: year Movement (X7) Number of landings or takeoffs at airportsY = β0 in+ aβ 4givenX4 + βyear7X7 ,(in thousands) (5) The estimated coefficients of the new model together with the 95% confidence interval are shown in Table7. All coefficients of the new regression model, as well as the regression model, are statistically significant (p-value = 0.003 < α). The value of the coefficient of multiple determination is 88.82%. Sustainability 2021, 13, 5396 14 of 17

Table 7. Estimated coefﬁcients of the resulting regression model (α = 0.05).

Coefﬁcient Estimate Standard Error p-Value 95% Conﬁdence Interval Intercept 1302.904 356.161 0.008 (604.841; 2000.967) Civil Planes (β4) −1.993 0.543 0.008 (−3.058; −0.928) Movement (β7) 7.792 1.919 0.005 (4.031; 11.552)

3.3.2. Poisson Regression Model (Model II) The equation of the Poisson model, which considers all input variables, is as follows:

7 ln(Y) = β0 + ∑ βiXi, (6) i=1 or β + 7 β β + 7 β Y = e 0 ∑i=1 iXi = e 0 ∏i=1 iXi , (7)

where β0, βi, i = 1, ... , 7 are the model coefficients. Output variable Y represents the total number of civil aviation occurrences in a given year. The result of testing indicated that variables X1 (Year), X4 (Civil Planes), X6 (Age) and X7 (Movement) had statistically significant effects on the number of CAOs. It seems that the best resulting model is as follows: Y = eβ0+β1X1+β4X4+β6X6+β7X7 , (8) The estimated coefficients of the new model together with the 95% confidence interval are shown in Table8.

Table 8. Estimated coefﬁcients of the resulting Poisson model (α = 0.05).

Coefﬁcient Estimate Standard Error p-Value 95% Conﬁdence Interval Intercept 11.043 0.823 2 × 10−16 (9.427; 12.63) −2 Year (β1) 0.029 0.012 1 × 10 (0.005; 0.052) −13 Civil Planes (β4) −0.011 0.001 4 × 10 (−0.014; −0.008) −3 Age (β6) 0.035 0.011 2 × 10 (0.012; 0.057) −16 Movement (β7) 0.038 0.004 2 × 10 (0.029; 0.046)

The model coefficients, as well as the resulting model, were statistically significant (p-value = 0.031 < α). The Pseudo-R2 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 βi means that as the value of variable Xi increases by 1 (with the remaining variables unchanged), the expected variable CAOs increase. A negative value of coefficient βi indicates that if the Xi value increases by 1 (with the remaining variables unchanged), the expected value of CAOs decreases. If the value of input variable X1 (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 X1 (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 X4 (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 X4 (there will be almost a negligible 1% decrease in the number of occurrences). An increase in variable X6 (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 X7 (Movement, in thousands). An increase in variable X7 by 1 (with the remaining variables unchanged) will also cause a very slight increase in the expected number of CAOs Sustainability 2021, 13, x FOR PEER REVIEW 15 of 18

variables. A positive value of coefficient 𝛽 means that as the value of variable 𝑋 increases by 1 (with the remaining variables unchanged), the expected variable CAOs increase. A negative value of coefficient 𝛽 indicates that if the Xi value increases by 1 (with the remaining variables unchanged), the expected value of CAOs decreases. If the value of input variable X1 (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 X1 (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 X4 (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 X4 (there will be almost a negligible 1% decrease in the number of occurrences). An increase in variable X6 (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 Sustainability 2021, 13, 5396 variable X7 (Movement, in thousands). An increase in variable X7 by 1 (with the remaining15 of 17 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% (exp(0.031) = 1.031 > 1). When the total number of aircraft movements increases by by1 (in3.1%. thousands), there will be an increase in the number of aviation occurrences by 3.1%.

3.3.3.3.3.3. Comparison Comparison of of Models Models TheThe following following step step comprised comprised a comparison a comparison of the of thereal real number number of CAOs of CAOs and the and the- the oreticaltheoretical (expected) (expected) number number of CAOs of CAOs obtain obtaineded from from the the models. models. A A graphical graphical comparison comparison ofof the the classical classical regression regression model model (Model (Model I) I) an andd the the Poisson Poisson regression regression model model (Model (Model II) II) is is shownshown in in Figure Figure 9.9.

FigureFigure 9. 9. GraphicalGraphical representation representation of of the the real real and and theoretical theoretical number number of of CAOs. CAOs.

BothBoth models models were were compared compared using using the the AI AICC value. value. The The lower lower the the value value of of the the AIC AIC criterion,criterion, the the lower lower the the residual residual components components of of the the model. model. Hence, Hence, such such a model a model exhibits exhibits a a better agreement with the empirical values of the dependent variable. The value of the better agreement with the empirical values of the dependent variable. The value of the AIC criterion for the multiple regression model was 106.29, while the value for the Poisson AIC criterion for the multiple regression model was 106.29, while the value for the Poisson regression model was 98.45. It is therefore possible to conclude that the Poisson regression regression model was 98.45. It is therefore possible to conclude that the Poisson regression model may be regarded as more appropriate. model may be regarded as more appropriate. 4. Conclusions The present study investigated occurrences in civil aviation which happened in Slo- vakia during the period from 2000 to 2019. The published statistics indicate that since 2017, the number of civil aviation occurrences in Slovakia has been increasing. While the number of serious incidents exhibited a downward trend, the number of incidents exhibited a dramatic increase. The percentage of incidents in the total civil aviation occurrences over the last 5 years reached the alarming level of almost 95%. It is therefore very important to investigate the causes of the incidents. The monitoring of civil aviation occurrences over 10 consecutive years in Slovakia facilitated the identiﬁcation of the most important categories of incident causes, including a collision with a bird or an animal, technical failures of aviation technology, unauthorised penetration of air space, laser and lost connection during the ﬂight. The information from the mathematical models can be applied to the accident risk assessment in civil aviation. The multiple regression analysis and the Poisson regression were used to create two models of correlations between the number of civil aviation occurrences and selected input variables for 10 years. Apparently, the Poisson regression model exhibited a higher quality than the model created by the multiple regression analysis. The model indicated, for example, that an increase in the number of commercial aircrafts aged over 14 years and an Sustainability 2021, 13, 5396 16 of 17

increase in the total number of aircraft movements significantly affect the increase in the number of civil aviation occurrences in Slovakia in a given year. Understanding civil aviation occurrences and their causes leads to a higher safety of air traffic. The experiences show that there are many different minor occurrences that may indicate the existence of a hazard and the development of a risk that might result in an accident. It is important to know such minor occurrences; that is why the relevant data should be collected and assessed to take adequate preventive measures. Each CAO is unique, and finding the causes of the event is not always easy. The proven method of preventing CAOs is the implementation of an integrated Safety Management System that allows a real change in the organisation’s ability to increase safety.

Author Contributions: Conceptualisation, M.A., D.M. and A.G.; methodology, M.A. and A.G.; software, M.A.; validation, M.A. and A.G.; formal analysis, A.G. and P.K.; investigation, M.A. and A.G.; resources, A.G. and P.K.; data curation, M.A.; writing—original draft preparation, M.A., A.G., D.M. and P.K.; writing—review and editing, A.G. and D.M.; visualisation, M.A.; supervision, D.M.; project administration, D.M.; funding acquisition, D.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Acknowledgments: This article was prepared with the support of the project titled VEGA 1/0429/18 “Experimental research of stress-strain states of rubber composites used in the mining and process- ing of raw materials” and the project titled KEGA 002TUKE-4/2019, “Modern technologies and innovations in the education of physics at FMT TUKE”. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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