Zieja Mariusz, Smoliński Henryk, Gołda Paweł: Estimating the system efficiency to ensure aircraft flight safety. Szacowanie efektywności systemu w celu zapewnienia bezpieczeństwa lotu statku powietrznego.

DOI 10.1515/jok-2015-0061 ESSN 2083-4608

ESTIMATING THE SYSTEM EFFICIENCY

TO ENSURE AIRCRAFT FLIGHT SAFETY

SZACOWANIE EFEKTYWNOŚCI SYSTEMU

W CELU ZAPEWNIENIA BEZPIECZEŃSTWA

LOTU STATKU POWIETRZNEGO

Mariusz Zieja, Henryk Smoliński, Paweł Gołda

Air Force Institute of Technology

e-mails: mariusz.zieja@itwl.pl, henryk.smolinski@itwl.pl, pawel.golda@itwl.pl Abstract: In the article was presented approach logical - probabilistic to assess the efficiency of the flight safety assurance system of aircraft considering that it is justified by the random nature of the process, which describe the indicators and logic is necessary during qualifying the threats and prevent such threats. Was proposed a method of quantitative estimation of system efficiency based on data and information collected in the information systems exploited in the Air Force. Was presented an analytical method for determining the probability of counteracting by the pilot emergency situation in-flight in cases where we have relevant data on the risks of flight safety. The probability of counteracting by the pilot emergency situation in-flight is even greater the higher the expected value and the lower the variance.

Keywords: flight safety, system efficiency, flight safety assurance, efficiency indicator

Streszczenie: W artykule przedstawiono podejście logiczno - probabilistyczne do oceny efektywności systemu zapewnienia bezpieczeństwa lotów statków powietrznych uznając, że jest ono uzasadnione losowym charakterem procesu, który opisują wskaźniki a logika niezbędna jest podczas kwalifikacji zagrożeń i przeciwdziałania tym zagrożeniom. Zaproponowano metodę ilościowego szacowania efektywności systemu na podstawie danych i informacji gromadzonych w systemach informatycznych eksploatowanych w lotnictwie wojskowym. Przedstawiono analityczny sposób wyznaczania prawdopodobieństwo przeciwdziałania przez pilota awaryjnej sytuacji, w przypadku, gdy dysponujemy odpowiednimi danymi. Prawdopodobieństwo przeciwdziałania przez pilota sytuacji awaryjnych podczas lotu jest tym większa im większa wartość oczekiwana i mniejsza wariancja.

Słowa kluczowe: bezpieczeństwo lotów, efektywność systemu, zapewnienie bezpieczeństwa lotów, wskaźnik efektywności

1. Introduction

Air safety is one of the important components of an effective management system of aircraft operations. Various adverse events generate losses in the aviation system and their estimation with appropriate indicators is necessary to evaluate the efficiency of the flight safety assurance system (FSA). This test was taken in this study proposing to assessment of efficiency a probabilistic- logical approach. The perfection of FSA system is determined by its quality, described by a series of appropriate indicators, including efficiency indicator, sizes which are determined based on the criteria for selecting the best, in a sense, their associations (optimal, setpoints, determined, permissible, acceptable, rational and others). FSA system is considered for the system "crew - aircraft" and its system environment (environmental, insurance, flights and logistics).

Under the concept of quality of the FSA system we understand the entirety of its properties (quality indicators) selected and justified according to its intentional purpose.

Taking into account the above statement, we can assume that efficiency is one of the indicators of the quality of directly characterizing the result purposeful use of the system concerned.

At present, methods of analysis and synthesis of flights safety assurance systems are insufficiently expanded. In practice, the operation of airlines and aviation companies, as well as the Air Force in the field of flight safety assurance are applied only the simplest statistical estimations, such as the average raid to damaged aviation technology, the average raid on the air event. Analytical methods for estimating the possible directions to incur expenses for FSA are not used.

2. The problem analysis of estimating the efficiency of the FSA system

Taking into account described above system of concepts was analyzed and made general characteristics of efficiency indicators of FSA systems [1], [2], [3], [4] which is necessary to a quantitative estimate and justify the requirements for rational variant of FSA system with a variety of output data, restrictions, solutions (decisions) technical and organizational, considering them on a background of a set of quality indicators. For this it is necessary to select and justify the nomenclature Π of quality indicators

p

k of FSA system, ie.:

K

k

p

_k





,



1

,

2

,...,

(1)

From the point of view of their impact on the efficiency of solutions facing the system tasks such indicators are well researched and formally defined, for example, lifetime reliability, resistance to interference, ergonomics, price, cost, etc.

An important distinguishing property of FSA systems is broad participation by staff personnel - pilots, professionals who control operation processes in the activities of FSA system to detect and neutralize negative impacts within a reasonable time.

The indicator system, on the one hand should be sufficient to estimating the efficiency of the FSA system with the necessary precision, on the other hand, should allow to make this estimation with the greatest ease.

FSA system efficiency indicator in addition to quality indicators depends on realization of the certain task by the system "crew - aircraft", after threat detection of the system and will be specified by certain size of WZBL, ie.:

W

ZBL





.

(2) As is clear from presented above analysis indicator the efficiency of the FSA

system is an indicator of overall, for which "work" all other quality indicators, in the sense that it characterizes the degree of achievement of the creation purpose of FSA system detecting within a reasonable time the threat in realization of air tasks and preventing (minimizing) the possible losses as a result of their implementation. Obtaining analytical dependence of efficiency indicator

W

ZBL of FSA system from the set П values of all other indicators of its quality, and from the set B of types of threats in realization of the tasks SP, the conditions

Ф of their implementation in

the form:

W



W

(



,

B

,



)

ZBL ZBL

(3) practically it is very problematic.

Therefore the indicator

W

ZBL

logically should be seen as a comprehensive property of the FSA system from the viewpoint of non-admission (minimizing) the emergence of losses in the "crew - aircraft" system in dangerous conditions of the air task realization. In terms of aviation training for so defined system such a threat may be the occurrence of damage (failures) to the SP, pilot error, weather conditions, etc., while the task realization. The main threat to the system when performing a combat mission apart from the above. is the threat posed by the enemy and this problem is not taken into account in these deliberations.

3. Quantitative measurement of the efficiency of the flights safety

assurance system of aircraft

Currently, testing and assessment of efficiency indicators of complex systems, which also includes the system of "crew - aircraft" and its FSA system, is carried out using the method of listening to experts (expert methods), statistical processing of information methods about the sizes of quality indicators of the system, physical modeling, mathematical modeling, and various combinations of these methods. Quantitative estimation (evaluation) of the efficiency indicator of FSA system can be made based on the analysis and processing of their statistics and information data regarding the risks of operation of the system "crew - aircraft" and their consequences (losses) for the system.

The authors in [4] propose a quantitative assessment of the efficiency indicator in the form:

As mentioned earlier in assessing the efficiency usually must take into account more than one measure therefore in assessing the choice of location should be taken into account other criteria, and as a result we get vector of efficiency assessments, ie.: , / 1 _{i i} ZBL i m M W   (4)

where: mi – the amount of the successful implementation of the evaporation of

threats of i-th type of the task realization  – the total number of i-th risks, and it is a deterministic indicator.

It seems advisable for the benefit of a quantitative estimate of the efficiency of the FSA system the application of a logical – probabilistic concept. This approach justifies the random nature of the process, which describe the indicators and logic is needed in qualifying the threats and prevent such threats.

If we take into account air events occurred due to damage to aircraft, flight safety then we can associate with the characteristics of reliability, for example. technical probability of events consisting on that that the technique has been damaged and the crew opposed the occurrence of their effects with some probability, and we can write [3]:              





i pi n i i n i t q BL P P q P P 1 1 1 (5) where: t

P

– technical probability of flight safety,

i

P

– probability of failure-free operation of i–th SP system,

i

q

– probability of damage of i-th SP system,

n – general (possible) the amount of such damage in flight.

The probability of damage and the probability of failure-free operation (proper operation) a certain i-th system on the fly (or at the relevant stage of flight) at time t is determined by the intensity of damage to the system (



i

)

according to data, which are calculated during the preparation, corrected during testing and specified in the process of exploitation.:

; . t q_i 



i (6) where: i



– failure intensity,       i pi q BL

P – the probability of prevention of emergency situations by the pilot

As a first approximation it can be assumed:







































i

t

i

t

i

n

n

t

i

t

b

e

e











1

1

1

1

₍₇₎ where: b



– intensity of air accidents caused by damage to SP on the fly, and















i pi i

q

BL

P



(8) or







  n i n i i n i b i 1 1 1 1      ₍₉₎

then the efficiency indicator of the FSA system taking into account the damage to the technique is as follows:







   _n itz n i itz n itz bt ZBL bt W 1 1 1 1      ₍₁₀₎ where: bt



– intensity of air accidents caused by damage to SP on the fly,

itz



– failure intensity of SP on the fly causes a threat to flight safety,

Efficiency indicator WbtZBL shows what part of damages of technique on the fly

leads to failure of the aircraft.

Above mentioned indicator can be extended to events arising from the mistakes of the crew or meteorological conditions encountered during the implementation of the air tasks and other threats, then the dependence (10) takes the form:







   _n io z n io io z n io z b io ZBL io W 1 1 1 1      ₍₁₁₎ where: ioz



– intensity of security threats of flights of i-th type, bio

Efficiency indicator WioZBL shows what part of the threats incurred during

implementation of the air tasks leads to an emergency situation causing losses in the system.

The probability of counteracting by the pilot emergency situation caused by i-th risk factor βio can be assessed by experts or in analytical way if we have the

relevant data, ie.:

       io pio io q BL P



(12) where: io

q

– probability of the emergence of i-th risk factor.

Fig. 1 Illustration of a function xi(t) of time of pilot reaction to the threat

With the occurrence of i-th risk factor, an emergency situation develops over time

aw

t

in order to achieve one of the defining coordinates

x

_i of acceptable limit x_idop

(Fig.1). The pilot can prevent a failure if the response time to failure t_r will be lower than the maximum permissible time t_dop.

Values

t

_aw, tr, tdop are the random values and are guided by rules of

decomposition

f

(

t

_aw

)

, f(tr) , f(tdop). r

t

t

_dop

t

_aw

t

)

(t

x

_i

idop

x

Time t_r is determined by information about the failure or identify failures and insufficiently fast pilot reaction in assessing the situation and taking action.

The probability of counteracting by the pilot an accident or other emergency factor. ) 0 ( ) (      _{ri dopi i} i P t t P t P (13) where: ri dopi i t t t    .

If there are known the distribution laws fr(t) and fdop(t) at independent

random values trand tdop, then the probability can be calculated from the

expression:















0

)

(

)

0

_{i i} i i

P

t

f

t

dtdt

P

_ (14)



      t f t f t t dt f( _i) _ri( ) _dopi( ) (15)

If the probabilities t_r and t_dop are normal then their ratio also gives a normal distribution 2 2 ( ) 2 1 ( ) 2 i i ti i t t i t f t e 





       ₍₁₆₎ where: i t

 – expected value  ti tdopit_ri;, ti 



– standard deviation, 2 2 dopi ri t t ti







_





,

and so the probability of counteracting failure by the pilot amounts to:

)

(

*

2

1

1

2 2 2 ) ( ti i i t t ti i

t

t

d

e

P

ti i i i          















 







  (17)

Probability of counteracting failure from i-th risk factor is the higher, the greater the expected value



t

_i and the smaller the variance

2

i

t



4. Conclusions

Problem of presented approach to efficiency assessment of the FSA system is the need to involve a large volume of statistics and team of experts to analyze threats and attempts to counteract them in application to different types of SP.

Increasing accuracy of quantitative estimate of the efficiency indicator of the FSA system is possible with assembling information obtained by various methods of research. In the nature of such information may be used, for example, the results of mathematical and physical modeling, corresponding to the estimation of experts and held statistical data of threats in the implementation of tasks by the system. The objective of further actions in this area can be specification of methods and the development of procedures for monitoring the efficiency indicators of the FSA system, taking into account supporting with appropriate information systems

5. References

[1] Babak, V.P. Caraczenko, V. O. Maksimow i inni. Pod redakcją Babaka V.P.: Bezpieka Awiacji: – Kijów, Technika, 2004.

[2] Kulavskiy V.G., Sharon V.D., Kudryavtsev A.A.: Zarządzanie eksploatacyjnym bezpieczeństwem w liniach lotniczych, BL. Nr 3.2011. [3] Smoliński H., Zieja M.: Logiczno probabilistyczna analiza czynników ryzyka

wypadku lotniczego. Wydawnictwo Naukowe Instytutu Technicznego Eksploatacji – PIB, Radom 2009.

[4] Volynsky V.Y., Volynsky-Basmanov Y.M., Michailov Y.B.: Metodologiczne problemy ilościowej oceny efektywności systemu zapewnienia bezpieczeństwa obiektów lotnictwa cywilnego, BL. nr 1.2012.

PhD. Eng. Mariusz Zieja, Polish Air Force, graduated from Military University of Technology in 2000. M.Sc. in Mechatronics specialized in Aircraft’s Avionics. In 2008 achieved Ph.D. in Mechanical Engineering. Since 2004 Assistant in Air Force Institute of Technology.

PhD. Eng. Henryk Smoliński, Polish Air Force, graduated from Military University of Technology in 1969. M.Sc. in Engines and Aircraft. In 1989 achieved Ph.D. in technical sciences in Construction and Operation of Machines. Since 1984 Assistant in Air Force Institute of Technology.

PhD. Eng. Paweł Gołda, Polish Air Force, graduated from Warsaw University of Technology in 2008. M.Sc. in Air Traffic Control. In 2013 achieved Ph.D. in technical sciences in Construction and Operation of Machines. Since 2011 Assistant in Air Force Institute of Technology.