The Method of Proactive Risk Assessment for Flight Safety Based on the Rate of Dangerous Events

: This publication is devoted to the issues of risk assessment in the safety management system of military aviation. The method of proactive assessment of risks to flight safety based on the number of dangerous events, which is based on correlation-regression analysis, provides an opportunity to predict the conditions that contribute to the occurrence of accidents. Studies conducted with this method have confirmed the dependence of the number of aviation accidents and serious incidents on incidents recorded for different groups of reasons, as well as on the intensity of flight activities. The obtained results can provide initial data for quantitative risk assessment in the safety management system of military aviation. The implementation of such an approach is appropriate in safety management systems in the transition phase from active to proactive approaches, until a sufficient information database on hazards is accumulated.


Introduction
Flight operation of aircraft is related to the risks caused by many factors. The main factor, along with economic and political, affecting the safe operation of military aircraft, is the effectiveness of the safety management system (SMS). The main task of the SMS is to control and manage the risk factors. The components of risk factor management for flight safety (FS) are the identification of hazards, as well as the development and implementation of effective and adequate measures to reduce their negative impact [1].

Flight Safety Risk Assessment of Military Aviation
The concept of risk by the international standard [4] is interpreted as the impact of uncertainty on the goals. In addition, the definition of risk is a combination of the consequences of events and the associated probability of events. ICAO documents define the risk in the field of FS as the presumed probability and severity of flight consequences [6]. It is almost impossible to predict the occurrence of an event in flight; however, having a sufficient database of observations of the results of flights can determine their intensity. The consequences of the hazards can be an accident, a serious incident, or an incident. Definitions of these events in the article are used in accordance with the terminology of ICAO [10].
The method of assessing the safety risk proposed by ICAO [6] involves the analysis of identified hazards. This requires the use of a comprehensive database of all hazards. Due to the small (compared to civil aviation) raid in military aviation, the manifestation of such risks will be a rare event, and the filling of an adequate database is a long process. The database of safety hazards is not maintained, but every dangerous event is recorded.
The classifier of incidents in the AFU identifies 15 types of their causes, which are grouped into three different groups: • the first group -incidents related to incorrect (erroneous) actions, violations of rules by personnel, • the second group -incidents related to failures of aircraft, • the third group -incidents related to the influence of external factors that are could not be predicted. Based on the database of flight operations in the AFU, the problem of risk assessment in the SMS will be solved by analyzing dangerous events and their intensity using the methods of mathematical statistics. To determine the dependence of the number of accident and SI on the number of incidents for different reasons, the method of correlation-regression analysis has been used. Therefore, it is necessary to determine the indicators and evaluation criteria.
The authors suggest that an increase in the number of incidents of a certain group of causes is an indication (signal) of the occurrence of conditions favorable for the commission of accident or SI. That is, the errors and violations committed by personnel have a greater impact on the number of accidents and the failures of aircraft on the number of SI. In addition, the number of accidents and SIs is affected by the intensity of flight activity.
The purpose of the authors' method of proactive safety risk assessment in military aviation is to determine the dependence of one FS indicator on another. The method has four steps, which can be conventionally designated as: I -Intensity, A -Average value, C -Correlation coefficient, R -Regression equation (IACR).
The initial data are absolute indicators of flight operation (flight hours, number of dangerous events, etc.).
In the first step, depending on the purpose of the assessment, based on the initial data of flight operation, it is determined by which indicators the assessment will be carried out. The following indicators are taken into account: type of dangerous events (accidents, SIs, incidents by types or groups of causes); time periods (year, month, etc.); types of aircraft (type of aviation: transport or tactical); level of assessment (Air Forces, aviation brigade, aviation squadron). After that, the intensity indicators λ are calculated and it is determined between which indicators the dependence, i.e. forecasting rules, will be established.
The second step is to determine the average values of ̅ λ̅ , which will be used to calculate the sample correlation coefficients. In addition, based on the average values of the indicators ̅ λ̅ , the limits of the confidence intervals of these indicators (λmin, λmax) are calculated as a criterion for the acceptable level of FS for these indicators. In addition, the sample standard deviation of the indicators is determined.
The third step is to calculate the correlation coefficients between the values of the evaluated indicators.
In the fourth step, the values of the obtained correlation coefficients for adequacy (whether the indicators really correlate with each other) are checked, and then the regression equation of the dependence of one indicator on another is calculated, as well as the coefficient of determination.
Finally, diagrams of the scattering of values of indicators are constructed and conclusions are formulated.
The obtained results are the initial data for quantitative risk assessment in the SMS of military aviation. International Standard [11] provides guidance on the selection and application of a sufficient number of risk assessment methods in a wide range of situations. Estimation (ranking) of the consequences of the influence of dangerous factors within the method is carried out in accordance with the approach proposed in [7]: from A -catastrophic to E -insignificant. Risk levels (acceptable, satisfactory, and unacceptable) are represented in a 5 × 5 consequence/probability matrix. Detailed descriptions of the proposed technique are followed.

Indicators for Assessing the Flight Safety of Military Aviation
During theoretical research, the level of flight safety is quantified by the following indicators [2]: Q -the level of risk (probability of accident); РFS -the probability of accident absence (probability of FS); tacc -the average flight hours to the accident (SI, incident) for the analyzed period.
ICAO notes that events are usually not tracked in absolute values, but in the form of occurrence frequency [5]. The authors consider this approach to be the most rational, so the paper proposes not to analyze the time intervals between events, but the number of events per unit of time (intensity). The experience of AFU shows that the intensity of dangerous events differs by 100 or 1 000 times, so for the convenience of analysis and perception of the results, it is proposed that each indicator determines its dimension, so that the values have no more than two digits after the comma, i.e.: To conduct certain statistical researches using information releases on air events and incidents for 1996-2017 years (in AFU), by Eq. (3) the value of intensity of occurrences for years of exploitation has been calculated (Tab. 1).

Tab. 1 Dangerous events intensity for 1996-2017 years
Year From Tab. 1 it can be concluded that the intensity of incidents and intensity of SIs have small distribution limits (0.87 ≤ λіnc ≤ 2.08; 0.50 ≤ λsi ≤ 2.45). At the same time, the intensity of accidents varies in a wider range (0 ≤ λacc ≤ 7.98) and is more random.

Determination of Confidence Intervals of Flight Safety Indicators of Military Aviation
To implement early prevention of accidents in the SMS, it is necessary to set thresholds, as well as the desired target levels for each indicator. They will serve as benchmarks for the unacceptable level of the indicator (intensity of dangerous events), or, conversely, the desired target (improved) level of frequency for such an indicator. As long as the trend does not go beyond certain limits, the number of such events will be considered acceptable (without deviations from the norm) for the relevant monitoring period.
To determine the limits of the acceptable level, a more appropriate method of the confidence interval was designed, which is calculated from observational data, and covers an unknown statistical parameter with a given reliability (confidence probability) [12]. We will assume that the probability of the indicator falling within this interval γ = 95% is sufficient for these studies.
To determine the limits of the acceptable level of the indicator, its average value and confidence interval are calculated according to the method below.
The average value of the intensity of incidents is determined by the formula [12]: where where tγ -the Student's distribution quantile tγ = f (γ, k), qγ -the normal distribution quantile qγ = f (γ, k), k -the number of degrees of freedom.
The results of the calculations performed for Eqs (4)- (7) are shown in Tab. 2.

Tab. 2 Characteristics of confidence intervals of incident intensity depending on their causes
Groups of causes of incident intensity From Tab. 2 it can be concluded that the highest intensity of incidents is recorded due to the failures of aircraft, as well as due to errors of aviation personnel. The limits of confidence intervals λ indicated in the table should be used when assessing the level of flight safety for a certain period as a criterion for assessing the level of safety -the limits of acceptable levels.

Determination of the Correlation Between Flight Safety Indicators of Military Aviation
Aviation events and incidents (failures of aircraft, aviation personnel errors, and the influence of external factors) are random events. As a rule, there can be a stochastic relationship between random variables, during which the distribution of another quantity Y changes with the change of the quantity X. The authors assume that the dependence between X and Y is linear. The most well-known measure of the linear dependence of the two quantities is the Pearson correlation coefficient.
Estimation of the dependence of the number of accidents and SIs on the number of incidents for different groups of reasons will be performed by the method of correlation analysis. To apply this method, the following conditions must be met: the sample must be representative, i.e. the number of observations must be sufficient; the parameters under study should be mutually independent and distributed according to the normal law [12].
Within the framework of this work, we will consider the results of all flight activities from 1992 to the present -the general set of events that occurred in the aviation of the AFU. Indicators of this activity for 22 years (from 1996 to 2017) can be considered as a representative sample.
The distribution law of intensity of incidents λіnc is defined graphically -on the histogram of this quantity size. To construct a histogram of the intensity of incident intensities ωіnc, it is necessary to determine the number of intervals of the histogram K (according to the Sturges rule).
where symbols   represent floor function. Since for Nc = 22 years, K = 7; the value of λinc is in the range of 0.87 ≤ λіnc ≤ 2.08; step interval Δlinc for density ωіnc, calculated: The results of the calculations can be Δlinc = 0.2. Using the data from Tab. 1 and by Eqs (8)-(9), the following histogram of incidents intensity was constructed (Fig. 1).

Fig. 1 Histogram of incidents intensity
According to the form of the histogram of the incidents intensity we can conclude that the general set of this random variable is distributed according to the law close to normal. Therefore, the fulfillment of conditions [12] to determine the relationship between indicators allows the use of correlation analysis.
A necessary and sufficient condition for the correlation of random variables X and Y is the inequality of zero correlation coefficient of the general set X and Y [12]: According to Eq. (11), pairwise Pearson correlation coefficients of flight safety indicators have been calculated. The results of the calculations are summarized in the matrix below (Tab. 3).  Number of accidents is more influenced by: • total flight hours (rxy = 0.74),

Tab. 3 Matrix of Pearson correlation coefficients of flight safety indicators of the Air Force of Ukraine
• number of incidents of the first group of causes (rxy = 0.68) and the intensity of these incidents (rxy = 0.3); this is due to the fact that the cause of 80% of accidents is the so-called "human factor", • intensity of flight activity (rxy = 0.56).
Number of SIs depends on: • number of incidents of the second group of causes (rxy = 0.82) which is due to the fact that most SIs are accounted for due to aircraft failures, The number of incidents of the first group (rxy = 0.8) depend on the intensity of flight activity. It is due to the fact that this increases the load on aviation personnel, which in these conditions makes more mistakes. To a lesser extent, tint affects the amount of accidents (rxy = 0.56) and the amount of SIs (rxy = 0.52).
To confirm the assumption of a linear relationship between the indicators of FS, the values of Spearman's rank correlation (nonlinear) coefficient were calculated for three pairs of indicators (Tab. 4). Tab. 4 shows that the values of the Pearson correlation coefficients are closer to 1 than the Spearman rank correlation. This means that the correlation between the indicators is rather linear than curve.

Tab. 4 Comparative
In this section, the values of the stochastic relationship between the indicators of FS were obtained. Next, to determine the mathematical model of this relationship, regression analysis should be used.

Regression Analysis of Flight Safety Indicators of Military Aviation
Regression analysis makes it possible to determine the functions of the dependence of the number of accidents and SIs on the number of the first or second group incidents. This allows you to predict the occurrence of conditions that contribute to the emergence of an SI or accident. The linear regression equation has the form: where α is the intercept, β is the regression coefficient.
To construct the regression line (12) it is necessary to determine the mean value of the number of dependent events (accident or SI) Y̅ and the prerequisites X̅ , "corrected", i.e. unbiased standard deviations sdy and sdx and the estimate of the correlation coefficient rxy.
The essence of the method of constructing a regression line will be considered based on the proposed assumption about the dependence of the number of accidents on the intensity of flight activity.
The first step is to calculate the values required to determine the dependence of the number of accidents (Y = nacc) on the intensity of flight activity (X = tint). According to Eqs (5), (6), and (11) and it is compared with the tabular critical value tγ (which is calculated according to the table of critical points of the Student's distribution [13] in accordance with the given level of significance αγ = 1 -γ and the number of degrees of freedom k =Nc -2).
If |Txy| < tγ -there is no reason to reject the null hypothesis, therefore, there is no correlation between random variables X and Y.
If |Txy| > tγ -the null hypothesis is rejected, therefore, the sample correlation coefficient rxy is significantly different from zero, i.e. X and Y are correlated.
The second step is to determine the coefficient and the free member of the regression: According to Eqs (12) and (14), we obtain: β = 0.0661, α = -0.7175. In addition, the equation of linear correlation has the form: Y = 0.0661 X -0.7175. Fig. 2 shows the scattering diagram (correlation graph) between the intensity of flight activity (tint) and the number of accidents (nacc) with the line of dependence. The coefficient of determination R 2 = rxy 2 shows the degree of correspondence of the proposed model to the real dependence between variables. The closer the value of the coefficient to 1, the stronger the dependence. For acceptable models, R 2 is assumed to be more than 0.5 (or 50%). In our case, R 2 = 0.3152. That is, the number of accidents depends on the intensity of flight activity only by 31.52%.
The use of this algorithm makes it possible to determine the mathematical dependence of one indicator on another one for any pair of Tab   The use of the method of regression analysis allows predicting the occurrence of conditions that contribute to the occurrence of SIs or accidents, and the degree of reliability of this prediction is characterized by value R².

Conclusions
The method of proactive assessment of risks to flight safety for military aviation by the number of dangerous events, which is based on correlation-regression analysis, provides an opportunity to predict the occurrence of conditions that contribute to the emergence of an SI or accident. The obtained results, in turn, will be the initial data for quantitative risk assessment in the SMS of military aviation. The introduction of such an approach is appropriate in SMS in the transition from active to proactive approaches, until a sufficient information database on hazardous factors is accumulated. The presented method makes it possible to take timely measures to prevent accidents, which will increase the efficiency of the FS.
Studies conducted by using the IACR method have confirmed the assumption of the dependence of the number of accidents and SIs on incidents recorded for different groups of reasons, as well as on the intensity of flight activities. They show that the number of accidents in 46.45% is affected by the number of incidents of the first group of causes (human factors) and in 31.52% the intensity of flight activity. The number of SIs in 67.07% is influenced by the number of incidents of the second group of causes (failures of aircraft). The number of incidents of group 1 depends on the intensity of flight activities by 63.47%.
As a criterion for the assessment of the FS level -the bounds of acceptable levels -it is proposed to use the limits of confidence intervals of incident intensity (λmin, λmax).
The direction of further research may be determining the best method of risk assessment, as well as the use of the application of Fuzzy Logic methods in determining the effectiveness of FS (the construction of membership functions of FS and the definition of a set of fuzzy rules). In addition, to improve the reliability of the results obtained when calculating the values of FS indicators according to this method, it is advisable to consider the types of aircraft, because the conditions of their flight operation (average flight hours, total flight time, etc.) are different.