ESTIMATION OF QUALITY PARAMETERS IN THE RADIO FLIGHT SUPPORT OPERATIONAL SYSTEM

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VITION ISSN 648 7788 / eissn 8 48 6 Volume 3: 3 8 doi:.3846/6487788.6.754 ESTIMTION OF QULITY PMETES IN THE DIO FLIGHT SUPPOT OPETIONL SYSTEM Oleksadr SOLOMENTSEV, Maksym ZLISKYI, Oleksiy ZUIEV 3 Natioal viatio Uiversity, Kosmoavta Komarova ve.

Educatio: Kyiv Istitute of Civil viatio, 97. ffiliatios ad fuctios: Professor i the Departmet of viatio Electroic Systems, at the Natioal viatio Uiversity, Kyiv, Ukraie.

Maksym ZLISKYI, ssoc Prof, PhD Eg Date of birth: 984. Educatio: Natioal viatio Uiversity, Kyiv, Ukraie, 7.

1 VITION ISSN / eissn Volume 3: 3 8 doi:.3846/ ESTIMTION OF QULITY PMETES IN THE DIO FLIGHT SUPPOT OPETIONL SYSTEM Oleksadr SOLOMENTSEV, Maksym ZLISKYI, Oleksiy ZUIEV 3 Natioal viatio Uiversity, Kosmoavta Komarova ve., Kyiv 368, Ukraie eduicao@au.edu.ua correspodig author eceived 8 pril 5; accepted 6 Jue 6 Oleksadr SOLOMENTSEV, Prof, Dr Sci Eg Date of birth: 949. Educatio: Kyiv Istitute of Civil viatio, 97. ffiliatios ad fuctios: Professor i the Departmet of viatio Electroic Systems, at the Natioal viatio Uiversity, Kyiv, Ukraie. esearch iterests: system desig ad processes i the operatio of radio-electroic meas, statistical aalysis of operatioal data. Publicatios: author of over scietific papers. Maksym ZLISKYI, ssoc Prof, PhD Eg Date of birth: 984. Educatio: Natioal viatio Uiversity, Kyiv, Ukraie, 7. ffiliatios ad fuctios: associate professor i the Departmet of viatio Electroic Systems, at the Natioal viatio Uiversity, Kyiv, Ukraie. esearch iterests: statistical aalysis of data i the radio-electroic operatioal systems. Publicatios: author of 45 scietific papers. Oleksiy ZUIEV, ssoc Prof, PhD Eg Date of birth: 966. Educatio: Kyiv Istitute of Civil viatio,989. ffiliatios ad fuctios: associate professor i the Departmet of viatio Electroic Systems, at the Natioal viatio Uiversity, Kyiv, Ukraie. esearch iterests: operatio of radio flight support facilities. Publicatios: author of 7 scietific papers. bstract. The paper cosiders the structure of the operatioal system of radio equipmet, determies the procedures related to the estimatio of the quality parameters i the radio flight support operatioal system, usig the ready-to-operate factor ad the probability of o failure operatio i a fiite time iterval, ad shows the aalytical ratios for the probability desity fuctio PDF. Keywords: operatioal system, radio flight support, the probability of o failure operatio i a fiite time iterval, ready-to-operate factor, estimatio.. Itroductio The groud facilities of radio flight support equipmet play a importat role i the process of providig regularity, safety ad efficiecy to civil aviatio etities. The operatioal stability of these facilities is supported with the help of the radio flight support operatioal Copyright 6 Vilius Gedimias Techical Uiversity VGTU Press

2 4 O. Solometsev et al. Estimatio of quality parameters i the radio flight support operatioal system system. The iformatio sigals i the operatioal systems are geerally radom. I order to solve practical problems ad to moderize the operatioal system, geeralized quality parameters are usually applied. These parameters are used to calculate the risks of air avigatio service, the threshold characteristics of radio flight support facilities, etc. The quality parameters of the radio flight support system iclude: ready-to-operate factor; operative factor; 3 techical applicability factor; 4 o-operative factor; 5 system itegrity; 6 cotiuity of fuctioig, etc. The iitial data required to calculate the quality parameters are statistical data, icludig the operatig time to a failure ad the recovery time for radio support flight facilities. The aalysis of some of the refereces to this article Nakagawa 5; Smith 5 showed that proper attetio has ot bee paid to the determiatio of the probability desity fuctio regardig the parameters give above.. Problem statemet.. Geeralized structure of the operatioal system The operatioal system is a set of products, operatioal facilities, executers, techological processes ad the documetatio that establishes the rules for their iteractio i order to effectively fulfill operatioal tasks. The operatioal facilities iclude buildigs, equipmet icludig tools, stads, devices, spare parts ad raw materials ecessary for operatio. The operatig system is a service type system, which is characterized by the flow of icomig ad outgoig requests. The icomig flow of requests З вх icludes separate tasks ad requiremets for them, for istace, a task of trasmittig iformatio o-board. The processig of requests is performed accordig to a specific techology which is implemeted i separate elemets techological systems of the air trasport system TS. The aalysis of the air trasport system shows that some techological systems TS iteract with each other o the basis of the maiteace priciple Kulyk et al.. example of the iteractio of some of the techological systems i the air trasport system cocerig the radio flight support FS is show i Figure. Figure shows the flow of icomig requests /3 3./3. from TS to TS 3, icomig requests 3./3.3 from TS 3. to TS 3., ad icomig requests from TS 3. to TS 3.3. I order to describe the requests, it is possible to apply the demad vector γ. This vector characterizes the requests by temporal demads parameter descriptio vector T, spatial demads parameter TS 3 ir Trasport System TS Users of TS service TS esource support system /3 /3 3/ OF TS 3. Flight performace system TS 3. System of radio flight support facilities operatio 3./3. 3./3.3 TS 3.3 System of maiteace ad repair of radio flight support facilities Fig.. Geeralized structural diagram of the iteractio betwee the techological systems i the TS

3 viatio, 6, 3: descriptio vector L ad iformatioal demads parameter descriptio vector I. Geerally, the umerical values of the compoets of the outgoig request vector γ differ from the umerical values of the compoets of the icomig requests vector γ because of failures or damages i products ad systems, the radom ature of the operatioal coditios, etc. s a result, the followig equatio ca be obtaied: /3 ã ; ;, 3/ LT I OF ã ' LT ; ; I ; 3./3. ã ; ;, 3./3. LT I ã ' LT ; ; I. OF To adequately describe ay TS, the followig compoets of the geeralized T S operator ought to be determied: the list of system elemets, the descriptio of which is give by the operator El ; the orgaizatioal structure of these elemets, the descriptio of which is give with the help of the geeralized operator Str ; system fuctioig coditios, the descriptio of which is give with the help of the geeralized operator C od ; resource supply, usig the geeralized operator es ; regulatory ad admiistrative documetatio, the descriptio of which is give with the help of the geeralized operator d ; iformatioal resources, the descriptio of which is give with the help of the geeralized operator Ir ; techological processes, usig the geeralized operator T P ; operatioal facilities, the descriptio of which is give with the help of the geeralized operator Om, icludig buildigs ad costructios geeralized operator Bu, meas of the techological equipmet geeralized operator Mte, which cosist of the mai techological equipmet ad techological tools. The geeralized operator for the TS 3. is described as follows: 3./3. 3./3. TS 3. Ò; ' γ; OF γ / StrEl;OmMte,Bu;T P ; Ir; Cod;e s;d. Havig set the parameters icluded i the descriptio of the radom geeralized TS operator, it is possible to observe the chages i the states of the system, specifically its phase states S tt i time. ccordig to referece Dhillo 6, it ca be presumed that the mai compoets of the operatioal system are as follows: requests to be processed; structural elemets of the operatioal system ad their orgaizatioal structure; techological processes; executors egieerig persoel maitaiig radio flight support facilities; operatioal facilities; admiistrative regulatory documetatio; osumables; iformatioal resources; operatioal coditios climatic coditios, electromagetic compatibility. The effectiveess of the operatioal system fuctioig ca be studied cosiderig two aspects. The first aspect is related to the impact of the risk o radio flight support facilities ad the stability of the air avigatio service system fuctioig. other aspect of effectiveess is related to the miimizatio of the costs spet o radio flight support facilities. To carry out a quatitative evaluatio of the radio flight support operatioal system fuctioig, it is ecessary ad possible to use the geeralized reliability parameters, i.e. the probability of o failure operatio i a fiite time iterval, ad the ready-to-operate factor, etc. Nechval et al.. ctually, these parameters are radom values which ought to be determied ad fully characterized i the form of the probability desity fuctio... Mai statistical characteristics of the probability of o failure operatio i a fiite time iterval It is kow that the probability of o failure operatio i a fiite time iterval Pt meas that o failure will occur if certai coditios i a give iterval of time or withi specific operatig time t exist. Geerally, the iitial data for the calculatio of the reliability idicators is the statistical data o the operatig time t i ad recovery time τ i for the radio flight support facilities. The iformatio pertaiig to the time betwee failures ca be comprehesive for calculatig the probability of o failure operatio i a fiite time iterval. ccordig to Kulyk et al., the case of expoetial operatig time betwee failures is believed to be most repetitive. The probability of o failure operatio i a fiite time iterval is determied by the followig ratio: t Pt e T, where T is the evaluated operatig time betwee failures. T ti. i This value correspods to the gamma distributio, which is described as follows: x x f x T Γ e, x, T T where is the umber of failures which is used i the evaluatio of the operatig time betwee the failures; T is the mathematical expectatio of the operatig

4 6 O. Solometsev et al. Estimatio of quality parameters i the radio flight support operatioal system time betwee failures; the Γ is a complete gamma fuctio. The probability desity fuctio PDF of o failure operatio i a fiite time iterval is calculated accordig to the followig ratio: dx f t, P f x. 3 dp x xp The iverse fuctio of the ratio ad its derivative are described as follows: t xp lp, 4 dx t dp Pl P. 5 pplyig formulas ad 5 to expressio 3 ad takig ito accout expressio 4, we derive the followig equatio: fter simplificatio, we obtai the fial expressio for the PDF of o failure operatio i a fiite time iterval: t t f t, P et l P, P. 6 PΓ + T l P The theoretical PDF ad the results of statistical modelig for the values of iitial parameters T, 5, t 5 are show i Figure. The omograms for the PDF of o failure operatio i a fiite time iterval for the case T, 5 for differet time itervals t are show i Figure3. f P Theoretical PDF esults of modelig Fig.. Theoretical PDF ad the results of statistical modelig t P f, t 5 t t 5 t 3 t Fig. 3. Nomograms for the PDF of o failure operatio i a fiite time iterval. P P Cosiderig the case of ormal operatig time betwee failures, the probability of o failure operatio i a fiite time iterval ad the evaluated operatig time betwee failures are calculated as follows: t t T σ P t σ π e dt ; 7 x T σ f x e, x. 8 σ π The expoet of equatio 7 is placed i a Taylor series to simplify calculatios, oly first two compoets of the series are take as follows: σ t t + 3t x 3tx + x 6σ π P. Upo solvig this equatio with respect to value x, the followig equatios are obtaied: 3 3 xp t+ 6σ π P 6σ t; 9 dx dp 3 3 σ π 6σ3 π P 6σt. pplyig formulas 8 ad to expressio 3 ad takig ito accout expressio 9, we obtai the followig: σ f t, P e 3 6σ3 π P 6σt t+ σ π P σ t T σ, P..3. Mai statistical characteristics of the ready-tooperate factor The ready-to-operate factor K uder the radom distributio of o-failure operatio time T ad recovery time T is equal to the ratio betwee the mea time of o-failure operatio ad the mea recovery time, which is described as follows: T K T + T. The revised calculatio of the ready-to-operate factor allows desigig complex systems more accurately, i order to implemet prevetive measures, to reasoably itroduce additioal elemets, etc. I additio, there is a possibility to optimize the umber of these elemets ad a more effective way to orgaize the maiteace of the ivestigated objects. The ready-to-operate factor K is estimated with the help of the followig equatio: T K T + T, where T ad T are the evaluated mea operatig time betwee failures ad system recovery.

viatio, 6, 3: 3 8 7 The followig equatio shows the PDF of the readyto-operate factor i the case of expoetial distributios of the operatig time betwee failures T ad recovery time T : K T T Γ K T T f K

4 If T T, the evaluatio of the ready-to-operate factor is submitted to the beta distributio: Γ f K K K whe Γ K.

6 4 + Figure 4 shows the results of the modelig for the case of expoetial distributios of the operatig time betwee failures ad recovery time uder the coditio that T, T, 5.

5 viatio, 6, 3: The followig equatio shows the PDF of the readyto-operate factor i the case of expoetial distributios of the operatig time betwee failures T ad recovery time T : K T T Γ K T T f K whe Γ T K T K, 3 G where is the umber of system failures i the observed time iterval, Γ is the complete gamma fuctio, a is the ormalizig factor: T T Γ x x T T a dx Γ T x T. 4 If T T, the evaluatio of the ready-to-operate factor is submitted to the beta distributio: Γ f K K K whe Γ K. 5 The average value of this estimatio is described as m K,5, which is stable; cosequetly, the dispersio is described as follows: µ K Figure 4 shows the results of the modelig for the case of expoetial distributios of the operatig time betwee failures ad recovery time uder the coditio that T, T, 5. The probability desity fuctio of the ready-tooperate factor estimatio for the case of expoetial distributio of the mea operatig time betwee failures T ad stable recovery timet is show i the followig equatio: T T T K K T T T K e + f K Γ K whe K. 7 The results of the modelig for this case T, T, 5, N 5 are show i Figure 5. f K Theoretical desity Experimetal Fig. 5. PDF ad of the ready-to-operate factor estimatio for the case of expoetial distributio of the mea operatig time betwee failures ad a stable recovery time Figure 6 shows the probability desity fuctio of the ready-to-operate factor estimatio for the case of ormal distributio of time betwee failures ad recovery time uder parameters T, T, 5, ad mea-square deviatio σ,t, ó,t. f K K f K Theoretical desity Experimetal K Fig. 4. PDF ad of the ready-to-operate factor estimatio for the case of expoetial distributio of the operatig time betwee failures ad recovery time K Fig. 6. Histogram of the ready-to-operate factor estimatio for the case of ormal distributio of operatig time betwee failures ad recovery time Cosiderig the case whe the ready-to-operate factor estimatio is carried out with oe failure ad oe recovery of the system where ad takig ito

8 O. Solometsev et al. Estimatio of quality parameters i the radio flight support operatioal system accout formulas 3 ad 4, the PDF of the estimatio is calculated as follows: T T f K whe T K T K.

6 8 O. Solometsev et al. Estimatio of quality parameters i the radio flight support operatioal system accout formulas 3 ad 4, the PDF of the estimatio is calculated as follows: T T f K whe T K T K. 8 The modelig results are give i Figure 7 T, T,, N 5. f K Theoretical desity Experimetal K 3. Coclusios The aalytical ratios obtaied durig the study are i good compliace with the modelig results. This fact cofirms the accuracy of these ratios. The research results ca be used i the desig ad moderizatio of radio flight support facilities. efereces Dhillo, B. S. 6. Maitaiability, maiteace, ad reliability for egieers. New York: Taylor & Fracis Group. 4 p. Kulyk, M.; Kucher, O.; Miltsov, V.. Mathematical models of the calculatio of aircraft structural reliability, viatio 5:. Nakagawa, T. 5. Maiteace theory of reliability. Lodo: Spriger-Verlag. 7 p. Nechval, N.; Nechval, K.; Vasermais, E.. Tolerace limits for reliability aalysis i maiteace problems, i viatio: appedix of Trasport Egieerig 5: 9 4. Smith, D. J. 5. eliability, maitaiability ad risk. Practical methods for egieers. Lodo: Elsevier. 365 p. Fig. 7. PDF ad of the ready-to-operate factor estimatio for the case If the operatig time betwee failures is equal to the recovery time T T та, the estimatio of the ready-to-operate factor is carried out accordig to the followig equatio: 9 The modelig results uder the coditio that T T ad are provided i Figure 8. f K Theoretical desity Experimetal K Fig. 8. PDF ad of the ready-to-operate factor estimatio for the case T T ad

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