Methods of assessing the reliability of restorable systems whose elements can exist in two states: a workable and refused (failure type "chain termination"), developed fully [1,2]. In those cases when it is necessary to improve the reliability of designed system without changing the reliability of components of its elements, usually injected back elements or groups of elements.
For a system consisting of elements that may be in three states, the introduction of redundant elements with three states can not only increase the reliability of the scheme, but even significantly reduce it. Everything will depend on the ratio between different types of failures, the circuit and the number of redundant elements. For most electrical items can distinguish the limiting cases of possible sudden failure, namely: chain termination and short circuit.
From the above it follows that the improvement of existing methods for calculating the reliability of complex systems on the structure, elements of which can be in three states and the development of new - is an actual scientific problem.
Improvement of existing methods for calculating the reliability of the structure - complex schemes taking into account the three states of the circuit elements.
A new method of obtaining of the probability of failure-free operation of the circuit, taking into account the failures of elements of type "short circuit".
The method of calculating the reliability of circuits substations taking into account the three states of electrical equipment.
Assessing the reliability of the system, whose elements can be in three states can be solved by using the algebra of tuples [5]. Computer simulation of complex circuits with two types of failures using many-valued logic leads to some difficulties in the transition from the logic function of efficiency of the system to a probability. Bringing the complicated structure of the schemes to a simple series - parallel may be using the methods of the triangle - the star and the star - triangle [6,7], what is spent considerable time.
All elements of the scheme may fail in operation independently. Items can be in three states: working and not working - refusal of type "chain termination" and "short circuit". These events are incompatible. Streams of failures such as "chain termination" and "short circuit" ordinary, stationary and without aftereffect. The probability of failure-free operation of the i-th element scheme is denoted Pi. Let qoi - the probability of occurrence of failures in the i-th element of type "chain termination", but through qsi - the probability of occurrence of failures in the i-th element of type "short circuit". Determine the probability of failure of the scheme R.
Denote the elements in a workable state structure scheme of character 
, not working 
,
where k - the code of failures, which takes two values. In the case when k = 0, then the element subjected to a denial type "chain termination", in that case, if k = s, then the element fails due to the failure of type "short circuit". Assume that the elements of the complex structure are subject only to the refusals of type "chain termination".
Consider a method based on the use of the theorem on the sum of probabilities of mutually exclusive events [8]. In the complex structure of the scheme to choose a base element (or group of basic elements). For such an element (or group) made the following assumptions: the basic element is in working condition and is absolutely reliable and main element is not working.
The probability of failure-free operation of the circuit consisting of n logical series-connected elements [6]:
(1),where n - number of elements in the scheme;
Poi - the probability of failure of the i-th element.
The probability of failure-free operation of the circuit, which consists of m logical series-connected elements:
(2),where m - number of elements in the scheme.
The resulting reliabilities Ro1 and Ro2 Ro2 for two schemes multiply: the first on the probability of failure-free state a basic element of Poi, and the second on the probability of failure Qoi basic element. The amount received by the two summands is equal to the probability of failure of a complex scheme (Ro).
The probabilities of failure-free operation with two types of failures is determined by the following formula [6]:
where Qoj - the probability of failures scheme taking into account the failures of type "chain termination";
Qsj - the probability of failures scheme taking into account the failures of type "short circuit".
Using the method described above, it is possible to assess the reliability of a complex scheme with two types of failures of the circuit elements: the refusal of type "chain termination" and the refusal of type "short circuit".
The proposed method of calculating the reliability of complex systems, elements which can be in three mutually exclusive states, allows to apply the usual logical and probabilistic methods without the use of transformations "star-triangle", as well as relatively complex concepts to engineers, such as the algebra of tuples.
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