Abstract:
The technical exploitation (TE) of aviation technique (АТ) concerns the execution of its technical service(TS). During the process of TS measuring of the value of basic parameters (BP) of the aviation comunication equipment (ACE) is done which creates the possibility of certain faults. The valuation of these faults and their limitation is a basic problem of TS and important aspect for maintaining high reliability and safety of aircrafts. Methods for determination of the limits of the faults and determination of the resource of aviation comunication equipment with the required level of probability are suggested in the paper.

Key words: statistical analysis; fault valuation; aviation communication equipment; reliability.

Problem Formulation: The regulation of the operating of ACE is related with periodic valuation of its sensitivity of the receiver and power of the transmitter. They determine the distance of the radio connection between the crews of the aircraft and the respective ground control center. During the TE of aircrafts of ACE, which is part of the whole radio electronic equipment (REE), different destabilizing factors may occur. That is why the valuations of the faults during measuring of BP of aircrafts are casual functions of the time.

Basic task for valuation of the flight time  is the valuation of the exploitation faults. In the accuracy and quality theory for technical systems, the function of the allocation of relative faults  during the measuring of the parameters  in the time t is written as a dense of allocation of the possibilities . The faults during the measurement of the parameters of ACE - , are located:
 
 

(1)

where: - the mathematical expectancy from N-measurements(N=10) of the value of the corresponding parameter of ACE, done at the same technical conditions;

- nominal value of the parameter under the tems of the normal technical documents(NTD) на ACE.
 

If this function is known, then the allocation of the parameters of ACE in the time is also known. But this is not enough to valuate the quality of ACE, because it may be used during different moments and periods of time. In a more general case the moments of time of usage of RЕE are casual values and have density of allocation . The laws for allocation of the times of usage of some types of REE of aircrafts during flight, characterized by the density of their allocation , are shown on fig. 1.
 
 
 

fig. 1. Allocations of the times of work of basic systems of the aircraft: 1- aircraft radio station, 2 – electronic altimeter set, 3 – navigational landing system

 

Because of the fact that the aviation communication station (ACS) and electronic altmeter are used regularly during the whole route of the flight, the allocation of the moments of time of their functioning is similar to the law for equal possibility. The equipment of the landing navigation system is used in the end of the flight, for the law for allocation of the moments of time of its usage is translated in the time to the end of the flight and is dependent on the normal allocation (fig. 1).

For the evaluation of the law for allocation of the fault with determination of the usage time, it is necessary to integrate the density of allocation of the fault  for all possible values of . In general the density of allocation of the fault can be written with the following integral:
 
  

(2)

where is a real number or infinity.

Knowing the characteristics of the fault during valuation of the parameters (mathematical expectancy, dispersion  or the field of diffusion of the parameters [2]), conclusions on the resources of the equipment with the necessary level of probability.

The mathematical expectancy of the law of allocation from (1) is dependent on:
 
 

(3)

 

where: - mathematical expectancy of the fault during a moment of time .

The dispersion of the obtained law for allocation from (1) is dependent on:
 
 

(4)

where: - initial moment form second series.

The initial moment from second series is calculated according to [3]:
 
  

, (5)

,(6)

The calculation of the analytic expression for in the interval [0;] is related with many difficulties.

Valuation Methods

Classic method, based on multiple measures

This method for locating the faults is based on the execution of N measurements of the same BP in a particular moment of time, at the same atmospheric and technical conditions and mutual independency between the different измервания. Practically for Military Airforces for N=10 a sufficient reduction of the casual faults during the valuation of BP of ACE is achieved [4]. The observation of the previous condition determines the simplification of the problem for valuation of the fluctuation of the BP ОП of ACE during particular periods of calendar time(1 year for the Bulgarian Airforces).

During the N measurements of particular BP in a particular moment (section) of time t,  from (1) can be represented through the normal law for allocation, in relation with the central boundary theorem from the theory of casual processes [3]:
 
 

, (7)

 
 Generally, the fluctuation of BP of ACE ® in the time is represented with a casual function and is shown on fig. 2:

 
 

fig. 2.

 

Fig. 2 reveals that the fluctuation of in defined moments of time can be approximated with a sufficiently smooth polynom or spline.

  The following formules for valuation of the mathematical expectancy  and the experimental средно квадратичното dimension  are consequences from (2),(3),(6) and fig. 1 and 2 [3]:
 
 

, (8)

 
  

, (9)

The graphics are based on measures, done for 1 year through intervals of 5 days for given by the standards requirements, but at the temperature (20± 1)° C[6]. They are statistically processed through the program MS Excel.
The volume of the measures allows a presentation sample and a precise definition of the characteristics of the communication equipment. The defined characteristics can be used for valuation of another similar equipment. The significant dynamic of the fluctuation of the parameters (30-40% in particular reviews) require enough accuracy for reliable definition of the resource of the equipment and to make difference between the reliable equipment and the equipment, needing replacement of functional elements.

This allows the achievement of significant economies without compromising the safety of the flights.
 
 

Fig. 3.а. Fluctuation of the sensitivity of radiostation Р-862 during measures, done for 1 year

Fig. 3.б. Fluctuation of the power of radiostation Р-862 during measures done for 1 year

Method based on the transformation to time parameters

This method for locating the fault during the measurement of BP of ACE is also valid for particular intervals of time, as his accuracy is increased when the examination is done for a shorter interval of time.

The law of allocation of the fault during the measurement of BP,  generally is function from K fluctuating in the time technical parameters:
 

, (10)

where:- temporary functions of allocation(mathematical expectancies) of the fault of К parameters in the time t .

The time t is written as a function , back to the function of the fluctuation of mathematical expectancies of j-th transforming in the time technical parameter. Using the transition to a new casual quantity  we obtain:
 

(11)

As the moments of time t are casual quantities, the parameter of the law for allocation (mathematical expectancy - ] will also be casual quantity. Therefore the full allocation of the fault  will be obtained through integrating the conditional law for allocation (10) for all possible values of the casual quantity :
 

, (12)

where:  - law for allocation of the quantity .

Using formulas (2),(10) and the ability to define of the law for allocation of the inverse function  knowing the law for allocation for the argument of the function , the law for allocation of the casual quantity  can be obtained:

  where: - function, обратна to the function  in the sections  , where its variation is monotonous and smooth enough.

By the same token as (12) we define the law for allocation of the function  when we know the law for allocation and from the formula (1)® as we find the density of the allocation of the fault during измерване of BP of ACE, according to:
 

(14)

where: - function, back to the function  in these sections  , where its variation is monotonous and smooth enough.

Example for the usage of the method using transformation into time parameters

Here we will review the valuation of the law for allocation of the fault during the measurement of BP of landing navigation system:

To simplify the calculations we assume that the admitted fault during measurement of BP of landing navigation system is done through a linear function - , e.g. (с-constant). The time for usage of this aviation system according to fig. 1 varies through a normal law:
 
 

Lets define the back function from the term of the example and its derivative according to:
 
 

We substitute these quantities and  in (13) and obtain the formula for evaluation of the law for allocation of the fault during the measurement of BP of landing navigation system:
 

where: 

CONCLUSIONS

1.The definition of the accuracy of the parameters of ACE and their fluctuation allows to valuate the status of the communication equipment with a high level of probability.

2. A precise analysis of the characteristics of the allocation of the parameters must be done because this, combined with the examined resource intervals is a basis for a quality measuring.

REFERENCES

1. Fomin A. N. and others,  Reliability of the semiconductor devices of aircrafts, Moscow, 1968.
2. Cvetkov A. F., Methods for valuation of the fluctuation limits of radioelectronic equipment", Москва, 1970.
3. Vencel. E. S. Calculus of Probability. Moscow, 1969.
4. Gindev E., Reliability of aviation electronic technique, “Air transport”, TU – Sofia, 1998.5. Petrov N. I., Bochev V. 5., Bonchev Kr. M., Radkov I. 5., Optimal Processing of Parametric Information for Regulation of the Technical Condition, High Military School "P. Volov", Shumen, 16.10.1997.
6. Schrьfer, E.: Zuverlдssigkeit von MeЯ- und Automatisierungseinrichtungen. Hanser Verlag, Munchen, 1984.