ESTIMATION OF TECHNOGENIC DANGER RISK OF TECHNICO- ECONOMIC SYSTEMS

Introduction: The risk as an event or set of events, holds a variety of discrete and/or ongoing implementations, each of which has its likelihood of occurrence and the amount of damage. The risk in modern science, culture and society is the summary category as sin, justice, value, meaning, etc. (Ivan Poptchev, Strategies for managing the risk of NBU, Sofia, 2004, p. 5, p. 6) [1]. Under the techno-economic system (TES) is a system of interacting manufacturing engineering (technology) equipment for automation and human operator [2]. The refusal of the FE of the TES is the reason for the technogenic danger (risk), continued throughout the period of technical operation (TO) of the systems [4]. For example, on the aircraft during flight is possible to be denied imposing performance of repair of the service crew, if the refused is not reserved with the FE upright one. In addition, the need to increase the technical resource of aircraft requires the placement of new technological systems (connected in parallel or in sequence of old), compatible with the available standard systems installed by the manufacturer. Similarly, is the State with the TES of a pipeline, the composite FE (units of pipelines) that pass through the village. It should be borne in mind that the maximum level of probability of failure of arbitrary complex TES is 10 -9 , i.e. on a billion connections in nature one of them failed [2].


Parallel connected FE of TES
For clarity of argument, it is considered that the constituent parts of the TES consists of two parallel United FE. The two FE are assumed to have constant intensity of flow of rejections, respectively for the first FE and for the second. As a component part of the TES store its working capacity, the unification of the FE assumes that is "loaded", i.e. is

Bulletin of Mathematical Sciences and Applications
Online: 2014-11-03 ISSN: 2278-9634, Vol. 10, pp 23-29 doi:10.18052/www.scipress.com/BMSA.10.23 2014 SciPress Ltd, Switzerland present"hot" reservation. Simultaneous failure of both FE is excluded. In these conditions is determined the intensity of the stream of rejections the component part of the system [6]: (1) If the intensity of the refunds on any FE of the components of the TES is constant and equal to for the first FE and for the second FE ( ), the intensity of the refunds of the component part will be determined by the [6]: (2) Since the probability of a safe condition the component part of the TES is defined by: where is the probability of dangerous condition (DC) of the TES in the same moment of time.
From formulas (1) to (3) follows the following differential equation (4) Equation (4) is decided in the performance of the condition: (5) corresponding to a safe condition at the beginning of the operation (t=0).
The decision of (4) is determined by the following formula: where is the probability that the component part of the TES to be recovered in the course of time t; -the probability for a faultless operation of the component part in the passage of time t.
Lets consider the marginal probability assessments for safe and dangerous (risky) status of the component part at a great value ( t) and small value ( t0) of operation time. , where is a constant. Such a combination of FE in reliability theory is known as "hot" reservation of basic (first) FE. In this case, the intensity of the denials of the components of the TES will have the form: (9) Accordingly, the intensity of the recovery is: where: is the intensity of the restoration of the FE.

Since
, it under (7) thies are determined: where: is the coefficient of readiness of the first FE; is the coefficient of stay of this FE. Therefore, the component part of the TES with "hot" reservation, the basic FE has limit value of the probability of safe (risk-free) status (at t), striving to on the primary node. Accordingly, the limit fixed value of the proba-bility of a dangerous condition is determined by the coefficient of this FE.
The limit values of the likelihood of a safe condition and the pro-bability of a dangerous condition of the TES at are determined from From these limit ratios, formula (3) and the Maclaurin expansion at t0 follows: (12)

Bulletin of Mathematical Sciences and Applications Vol. 10
where A,a are positive constants; -infinitely small quantity of a higher order of magnitude than Here the question arises what are the values of A and in a limit case, i.e. at t0. In this connection, we prove the following theorem. Theorem 1. If the constituent parts of the TES contain two parallel charged FE, the intensity of the refusals, which are and for the probability of safe and dangerous state of its constituent parts will be fair the following ratios: (13) Before the proof of the theorem is noticeable that by formula (13) in the t0 derive the following estimates of the probability of safe and dangerous condition of the components: In accordance with the formulae (1) and (2) it follows that Taking into account the above fact and (5) in the ratio of differential equation (4) is determined By the recording of (4.5.5) and (4.5.15) follows: For the determination of the value of the using differential equa-tion (4), which follows: From equation (1) follows , and from (17) follows equation Put the last expressions in (16) and receiving the first formula (13). Using (3) gets the second proof (14). This completes the proof of Theorem 1.
By guest on (14) it is noticeable that at small times of operation (valid especially for the aircrafts), the probability of safe and dangerous condition of the constituent parts of the TES (having parallel laden combination of FE) only depends on the intensity of the refusals of FE and does not depend on the intensity of the restoration. The physical nature of this phenomenon lies in the fact that in the home stretch of the exploitation of the constituent parts of the system reliability of FE property prevails and not the reimbursement of work ability.

Consistently United FE of the TEC
The overall assessment of the likelihood of safe and dangerous condition of the TES is done as for the simplicity of the argument it is assumed that the component consists of two successive United FE. The denials of FE are independent of each other and have a constant intensity. The intensity of the restoration of the composite part is constant and equal to . It follows the following theorem.

Theorem 2. Let the component part of the TES to contain two consecutively United FE that the intensity of the stream of rejections is accordingly and . Then the probability of safe and dangerous condition of the component part will be fair the ratios:
(18) Proof: In accordance with formulas (6) and (3)

CONCLUSION
The result of the study of dangerous and safe condition of reimbursable TES is created with a method implementation in technical exploitation of the air force and civil aviation [6]. Proven are two theorems and are possible the following generalizations: 1. At small times of operation (valid for aircrafts) relative to the total technical resource, the likelihood of safe and dangerous condition of the constituent parts of the studied systems (with parallel laden combination of elements) depends only on the intensity of the failures of the same and does not depend on the intensity of the restoration.
2. The fixed value of the probability for the safe condition of the TEС, with parallel laden connection of items in continuous service aspires to the coefficient of the readiness of most reliable item.
3. The limit fixed value of the probability for the safe condition of the TES, with a consistently united functional elements in continuous service strives to the coefficient of the readiness of its main (base) part.
Nikolay Ivanov Petrov received M. Sc. Degree at the National University "V. Levski" -V. Tarnovo, Aviation Faculty. On 10 January 1996 he has been conferred on PhD by dissertation work on the topic "Synthesis of functional and stochastic methods and systems for diagnostics and repair of air radio electronics and control and measurement installations".
On 10 April 2002 he has been conferred on Dr.Sc. by defense of the dissertation on the topic "Optimization and management of the technical exploitation of air systems". On 01.10.2004 he has defended successfully diploma project for a master on "Economics" at University for National and World Economy -Sofia.
In 2007 he was awarded Professor of the Trakia University on specialty ,,Atomized Systems for Treatment of Information and Control". He has more than 400 scientific works, publications and developments, 100 of which -abroad. He has published 35 scientific books and textbooks, 15 of which -monographs.