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5TECHNICAL SCIENCES
INVESTIGATION OF A STATISTICAL METHODS FOR QUANTIFYING THE CURRENT LEVEL
OF FLIGHT SAFETY
Abdalla A.
Flying Akademy of the National Aviation University, Kropyvnytskyi
Lytvynenko M.
Ivan Kozhedub Kharkiv National Air Force University
Smelyakov S.
Ivan Kozhedub Kharkiv National Air Force University
ABSTRACT
The problem of a statistical methods for quantifying the current level of flight safety is proposed to be solved through a probabilistic approach to both single-parameter and multi-parameter (integral or cumulative), both direct and indirect assessment of the level, both in the airline, and in the department or aviation industries on a national (regional) scale. Quantitative assessment is traditionally performed according to generally accepted standardized indicators (statistical and probabilistic), using mostly methods known to specialists: - calculated - when assessing the level, as a rule - for the group of factors "aircraft" at the stage of development and certification of the type of aircraft; - statistical - in a posteriori estimation and forecasting of the level based on the results of tests and operation; -expert - with a priori assessment and prediction of the level according to the conclusion of specialists. Estimates of indicators, obtained initially by calculation methods, are a posteriori refined as information on the results of tests and operation is accumulated. By the end of the operation of the type of aircraft, the estimates of indicators are approaching their true values. The task of a priori estimation like most tasks related to the assessment of the risks of accidents and disasters, is generally incorrect, since it is characterized by: - high level of uncertainty and variability of parameters reflecting the current and prospective levels; - lack of reliable objective information and initial statistical data; - dynamism and multifactorial dependence of the level. The variance of the current values of the frequency of aviation events (for example, with a monthly assessment) can be two or more times greater than the mathematical expectation (or the average annual value). The scatter of observed values of estimates of the probability of an aviation event has both a random component and a deterministic one, due to a regular change in the level, which occurs due to the dynamism of the aviation system in operation. To identify changes in the indicator and identify systemic changes, you can use the moving average method, which allows you to smooth the "peaks" in the current values of the indicator.
Keywords: method, flight safety, aircraft, airport, system.
1. Introduction
With the current (monthly) assessment airline in terms of the frequency of incidents, in order to avoid smoothing out deviations due to changes in the level, it is advisable to limit the smoothing length to three months, as shown by the results of optimizing the smoothing coefficient in the airline [1]. This use of a moving average allows you to identify trends and predict changes in the level according to the most appropriate indicator for evaluation. When quantifying the level, as a rule, so-called point estimates of indicators are found. However, any point estimate has a fundamentally significant drawback, since is itself only a partial value of a random variable. The degree of confidence in such an assessment and the degree of its accuracy may well be questioned. Naturally, the reliability of the zero estimate of the frequency of aviation events in the absence of such events depends on the number of flights performed. The accuracy of any indicator estimate is characterized by a confidence interval, and reliability is characterized by a confidence probability.
When designing a new, or analyzing existing, of the incident during the year, there emerges a task to evaluate data flow rate, and, in this case, the volume of multimedia traffic often turns out to be the largest and even decisive. When designing of the incident during
the year, in order to estimate the characteristics of data flow, a variety of mathematical models of traffic are typically applied [2-5]. However, such an approach is justified only if the constraints in the mathematical models themselves are met, such as, for example, sta-tionarity, ordinarity, and the absence of aftereffect for the Poisson stream of packets, etc.
A real pattern of the estimation of the incident during the year can only be obtained by experimental observations with compulsory subsequent statistical processing. This will not only make it possible to obtain the desired characteristics, but also to assess the reliability of the results derived.
2. Analysis of literature and problem statement
In modern conditions, characterized by an increase in the fleet of aircraft and an increase in the number of types of aircraft in operation, the problem of training flight personnel with the required qualifications has become aggravated in the leading airlines of the world. This is confirmed by the accidents that occurred with Boeing-737 aircraft in the commercial aviation worlwide.
Naturally, for any airline, intensive growth, accompanied by the development of new types of aircraft for the airline, new routes and airfields, is a well-known accident risk factor mainly in terms of the "Human Factor", and out of almost 80% of accidents and disasters,
on average, 25- 30% [6]. (According to other data, the share of erroneous actions of flight personnel among the causes of accidents reaches 70% or more [7]). Internationally, it is recognized that at least three of. four incidents are the result of errors, admitted by apparently healthy individuals with proper qualifications [8].
In the context of crisis phenomena, the problem in commercial aviation is exacerbated by the forced desire of operators to achieve maximum efficiency in the flight operation of air transport. An obligatory, but the most difficult condition for the prevention of accidents is the training of pilots of the appropriate professional level while reducing the time and costs associated with training, commissioning, professional growth, including admission to flights on new types of aircraft, when appointing aircraft commanders, instructors, etc. To some extent, the solution of commercial problems periodically conflicts with the provision of the required level, since the risk of an aviation event increases as a result of insufficient professional training, which causes flight parameters to go beyond operational limits [9].
When determining the professional level of a pilot (the degree of his compliance with the required level of safety in terms of the "Crew" factor), a specific decision is made on the basis of a subjective assessment of the degree of readiness of the pilot for solo flights (or for instructor work). The use of the functionality of onboard means of recording flight information (FI), hardware and software for processing FI, including express analysis, contributes to an increase in the objectivity of assessing the quality of piloting in each individual flight. It is natural to determine the achieved professional level based on the total number of flights performed, which differ from one another in the degree of complexity and, consequently, in the degree of potential success (danger), i.e. an appropriate database should be maintained.
When quantifying and predicting the level in a corporate base, the greatest difficulty is estimating the probability of an accident by the "Crew" group of factors due to the significant dependence of this parameter on the functional reliability of pilots, i.e. on the quality of piloting. One of the most significant characteristics of piloting quality is the probability of piloting without going beyond the operating limits.
Flight parameters that are subject to operational restrictions are obligatorily recorded in the onboard data storage devices. Subject to processing and analysis in at least 90% of flights. Modern hardware and software for processing makes it possible to accumulate in the database the extreme values of flight parameters obtained by express analysis, including those for which operational restrictions have been introduced. Thus, it seems possible to estimate the probability of piloting parameters going beyond the operational limits - based on the total number of flights performed by each aircraft commander (pilot).
Formulation of the problem. This paper proposes the results of investigation of a statistical methods for quantifying the current level of flight safety.
3. The aim of the study
The aim of the study is to develop investigate of a statistical methods for quantifying the current level of flight safety.
4. Estimation of the probability of flight parameters exceeding operational limits
Estimation of the probability of a random function of extreme values of a controlled parameter going beyond the limit of a certain value, located in the immediate vicinity of the average value of the observed population is not difficult for any distribution law [10]. But the value of the operational limit of the parameter and the center of distribution of its observed extreme values usually turn out to be more than 33 apart from each other. In practice, determine the distribution function of a random variable; outside of fails due to the lack of initial data (i.e., the task is to estimate the probability of an event that was not observed during the study period). Moreover, the form of the distribution function of a random variable outside the practically does not depend on the form of this function in the vicinity of the mathematical expectation. This confirms the need to choose a universal distribution function with the determination of its parameters directly from the results of observations.
Extension of the distribution function P( Xextr)
beyond the point (Xextr.n, Pn) up to intersection
with the X lim vertical would make it possible to obtain the desired estimate of the probability that the characteristic parameter does not exceed the introduced operational limit, i.e. get the value of the function P(Xextr) . But regardless of the method of restoring or extrapolating the function P(Xextr. lim), it is impossible to obtain a single-valued distribution function on the interval [Xn, Xum] due to the high degree of uncertainty, which is reflected by multiplying the options at some (extreme) point (Xextr.n, Pn).
In cases where the extreme values of the characteristic parameter X in different realizations (observations) do not depend on each other (as a rule, these are different flights or different stages of the flight), and the random variable X is not limited either on the right or on the left, the distribution law is described by the function [11]:
P(Xextr)= p(Xextr < Xextr.t) (1)
where p (Xextr < Xextr.t) is the probability of
not exceeding the independent variable Xextr.t
From (1) it follows that the normalized deviation is related to the Xextr argument through the statistical probability P(Xextr):
Y = - ln[-ln P( Xextr) (2)
In coordinates (Xextr.n,Y), i.e. Xextr,{-ln[-ln P( Xextr)]} points
(Xextr.n,Y) are located not on the interrupted
exponent, but on a straight line, the extrapolation of which to the value (Xextr.n, Y) allows you to get the
value (Y lim).
According to it - and an estimate of the probability of not exceeding the operational limits, using formula (1).
If the total number of flight parameters that have operational limitations on a particular type of aircraft and are recorded in the onboard storage is m, then the probability that the characteristic parameters will not go beyond the operational limitations in the upcoming solo flight is:
P = Pj (3)
By the expert method, the characteristic parameters that have operational limitations and most affect in civil aviation include:
- vertical overload (n.y) on landing;
- roll angle (g);
- takeoff pitch angle (Vland);
- landing pitch angle (V. t).
Probability of exceeding operating limits for at least one characteristic parameter in flight:
Q = 1 - Pi (4)
The feasibility of a probabilistic approach to assessing rare events accompanied by flight parameters exceeding operational limits is confirmed by statistics: for each flight, pilots make an average of 1.84 errors, while the maximum number of errors at the flight stage is 14 [12]. This indicates a significant difference between the average statistical value of the quantitative indicator and its extreme value.
Estimating the probability of extremely rare and unlikely events is extremely important in accident risk management, i.e. in preventive flight safety management within the acceptable (established in the airline, department, industry) level.
The list of flight parameters can be expanded by the user during operation. The limit values of the parameters (limitations) can be adjusted if necessary. The automated system makes it possible to carry out an analysis for each pilot individually, depending on the type of the manned aircraft, the aerodrome of departure and landing, in a given time interval (number of departures). Calculations can be made for the entire population or for any of the controlled parameters.
The results obtained can be used for an objective assessment of piloting, which allows timely monitoring of the level of training of the flight crew and promptly taking appropriate measures if the risk of an aviation event for the "Crew" group of factors exceeds the established (acceptable) level.
5. Development of a technique for indirect estimation of the probability of an aviation accident on the basis of a set of events
ICAO recommends the number of fatal accidents, i.e. aviation accidents per 100,000 sorties or hours of flight time.
The traditional methodology for calculating the level indicator provides for the presence of a certain number of a certain (selected) type of aviation events during the estimated period, but they are relatively rare.
The starting position of the probabilistic approach to indirect estimation of the frequency of aviation accidents was the reliably established sufficiently high correlation of quantitative ratios in the hierarchy of aviation events of varying severity [7, 12]:
- human casualties, i.e. disaster (D);
- without human casualties, i.e. accidents (Av);
- serious aviation incidents (SI);
- aviation incidents (I);
- precursors of aviation incidents (PI), i.e. events that are not subject to classification under the definition of "incidents", but affecting with the corresponding unfavorable development of the situation: failures and malfunctions with consequences, the influence of adverse factors of the "environment" group, erroneous actions or inaction of personnel, etc. - this category of aviation events is not is generally accepted, because does not have an official general definition, therefore, it can be introduced by aircraft operators for internal use within the framework of a corporate SMS on an initiative basis.
The listed aviation events in one flight can be considered as corresponding to the conditions of incompatibility and ordinaryness. Each aviation event, which is below the "K" event in the hierarchy, has a certain probability of developing into "K". Since all aviation events that took place in the estimated period of aircraft operation can be considered independent of one another, then the probability of an event "K" in flight falling on the estimated period of operation is generally represented as the sum of the accident probabilities for each of the identified aviation events:
m n
P . k= I I P . ij (5)
i=1j=1
where Pij - the probability of the event "K" at the i-th event of the y-th type;
i - the number of the aviation event of the y-th
type;
j - the event type number, j=1,2,...,n;
m - the considered number of aviation events of the j-th type;
n - the number of types of events selected for evaluation (when estimating the probability of an event of type "K", in the general case, one can limit oneself to n = 4: aviation accidents without human casualties, serious aviation incidents, aviation incidents, precursors of aviation incidents).
The probability of the event "K" for each i-th event of the y-th type is expressed through the conditional probability:
Pij = P( A.ij)P( A / Aij) (6)
where P(A.ij) is the probability of the i-th aviation event of the j-th type in flight;
P(A / A.ij) - the probability of the event "K", provided that the event ( A.ij) took place (happened).
As applied to the aircraft operator, the practical quantitative assessment of the level by the probability of an event of type "K" in flight provides for the assessment of the probability of an event "K" for the entire set of aviation events that took place in the estimated period. Flights performed by an aircraft operator without accidents turn out to be absolutely safe, which, of course, is not true. Therefore, if the airline does not have aviation events of any type in the estimated period (first of all, types "K" and "Av"), the probability of an event that is possible (not impossible), but not observed in the estimated period, can be determined by the formula [10]:
P = 1-VT-B (7)
where B confidence probability with which the estimation is performed, in the field of flight safety it is advisable to perform the estimation with B = 0.95.
When a posteriori estimating the probability of an event of the type "K" for the estimated period of flight operation (month, quarter, year, ...), as P(A.ij) one should use the statistical probability of the aviation events P( A.ij) or their frequency of manifestation (the number of events related to the number of flights performed).
6. Conclusions
Thus, it is possible to draw the following conclusions:
1) a significant increase in the reliability of estimating and predicting the level is achieved by spectral analysis of statistical data with the construction of a histogram of the frequencies of the distribution of estimates of the probability of incidents;
2) the effectiveness of using the apparatus of statistical and spectral analysis is obvious when using indicators that reflect the frequency of aviation events, but not indicators such as "aircraft event flight" and "number of flights performed per aviation event";
3) during estimating the probability of aviation events that did not take place, due to the flight parameters exceeding operational limits, it is advisable to use the apparatus of extreme statistics;
4) the unity of the approach to assessing the acceptability of the accident risk at the state and corporate levels is achieved by using the method of indirect estimation of the frequency of accidents, the initial position of which is a reliably established high correlation of quantitative ratios in the hierarchy of aviation events of varying severity;
5) conditional probability of the transition of an aviation event from a type with less to a type with more severe consequences depends to a large extent on causal factors;
6) the ratio of the causal factors of aviation events is variable, largely dependent on the degree of development and level of maintenance in aviation, and therefore requires correction with a frequency of no more than 5 years;
7) in case of insufficiency of statistical data in the airline, it is advisable to use the method of expert assessments.
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