Consider the complex structure of the scheme. All items that are included in the scheme may fail in operation independently of each other. Elements that comprise the scheme may be in three states: operable and inoperable – the refusal of the "open circuit"and "short circuit". These events are incompatible. The flow of failures of the "open circuit"and "short circuit" the simplest. The capacity of elements is unlimited. State probability of i–th circuit element is denoted by pi. We denote qoi – the probability of failure in the i–th element of the "open circuit" and, through qsi – the probability of occurrence of failures in the i–th element of the "short circuit". These three states form a complete group of events: pi + qoi + qsi = 1.
Real technical systems do not always represent a set of consistent and parallel connected elements. There are also more complex systems, for example, if a part of the scheme includes at least one "bridge structures", such a scheme is complex (Fig. 1) [2].
Real technical systems do not always represent a set of consistent and parallel connected elements. There are also more complex systems, for example, if a part of the scheme includes at least one "bridge structures", such a scheme is complex (Fig. 1) [2].
Abstract
Topicality
Problem statement
The method of minimal cutsets
The method of decomposition of the complex structure with respect to the basic elements
Visual representation of the method
List of references
Problem statement
The method of minimal cutsets
The method of decomposition of the complex structure with respect to the basic elements
Visual representation of the method
List of references
Topicality
Unrecoverable system in operation – it is such a system restore which for some reasons it is impossible at this time, [1].
Methods of assessing the reliability of such systems, whose elements can exist in two states: a workable and refuse (refusal of the "open circuit"), designed to fully [1,2].
In those cases where it is necessary to increase the reliability of designed system without changing the reliability of the components of its elements, is usually administered excess (reserve) items or groups of items, or make certain changes to the scheme, which allows to optimize its structure.
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 circuits, but even significantly reduce it. Everything will depend on the relation between different types of faults, the circuit and the number of redundant elements.
For most electrical items can distinguish the limiting cases of possible sudden failure, namely: open circuit and short circuit. For example, in the capacitor termination conductors soldered to the plates, reducing its capacity to zero (failure of the "open circuit"), or an increase in leakage current than the maximum value, the breakdown of the capacitor (the refusal of the "short circuit").
Failures of the diode can also be divided into two types: cracks in the diode, resulting in chain termination (failure of the "open circuit") and a short circuit in the diode (rejection of the "short circuit"), etc.
For relay–contact elements of various types and contactless relay breakage and short circuit are not marginal, but the only possible type of inoperable [3].
Elements with three states can be identified in other systems, such as: fire water lines, air ducts, pipelines, cooling systems of nuclear reactors, etc.
Analog elements with three states in such systems can be: taps, valves of various types, stop valves, plugs and other choppers flow, for which an inoperable state flow is not interrupted ("short circuit"), or not passed ("open circuit") .
Calculation of reliability of complex schemes for the structure with two types of failures can greatly improve the accuracy of calculations and to explain the mechanism and causes of multiple failures in the scheme.
Under the multiple failures meant the failure of several elements of the same reason [4].
Methods of assessing the reliability of such systems, whose elements can exist in two states: a workable and refuse (refusal of the "open circuit"), designed to fully [1,2].
In those cases where it is necessary to increase the reliability of designed system without changing the reliability of the components of its elements, is usually administered excess (reserve) items or groups of items, or make certain changes to the scheme, which allows to optimize its structure.
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 circuits, but even significantly reduce it. Everything will depend on the relation between different types of faults, the circuit and the number of redundant elements.
For most electrical items can distinguish the limiting cases of possible sudden failure, namely: open circuit and short circuit. For example, in the capacitor termination conductors soldered to the plates, reducing its capacity to zero (failure of the "open circuit"), or an increase in leakage current than the maximum value, the breakdown of the capacitor (the refusal of the "short circuit").
Failures of the diode can also be divided into two types: cracks in the diode, resulting in chain termination (failure of the "open circuit") and a short circuit in the diode (rejection of the "short circuit"), etc.
For relay–contact elements of various types and contactless relay breakage and short circuit are not marginal, but the only possible type of inoperable [3].
Elements with three states can be identified in other systems, such as: fire water lines, air ducts, pipelines, cooling systems of nuclear reactors, etc.
Analog elements with three states in such systems can be: taps, valves of various types, stop valves, plugs and other choppers flow, for which an inoperable state flow is not interrupted ("short circuit"), or not passed ("open circuit") .
Calculation of reliability of complex schemes for the structure with two types of failures can greatly improve the accuracy of calculations and to explain the mechanism and causes of multiple failures in the scheme.
Under the multiple failures meant the failure of several elements of the same reason [4].
Problem statement
Figure 1 – The bridge structures
In the bridge structure elements are connected in such a way that its further simplification is not possible with the help of elementary transformations (using the formula for evaluating the reliability of series and parallel connection of cells). Maybe convert the approximate or exact methods using transformation of delta–star, star–delta [3].
To assess the reliability probability of R (t) of Fig. 1 using a personal computer, for a time t proposed a method based on the methods: the minimum cutsets and a theorem on the sum of probabilities of incompatible events (the method of expanding the group of elements).
To assess the reliability probability of R (t) of Fig. 1 using a personal computer, for a time t proposed a method based on the methods: the minimum cutsets and a theorem on the sum of probabilities of incompatible events (the method of expanding the group of elements).
The method of minimal cutsets
The method of minimal cutsets is the first part of the algorithm.
There are some groups of elements, the simultaneous failure of which leads to the rupture of all paths connecting the input and output structures. A set of elements whose failure leads to failure of the structure (ie, breaking all links between input and output) in the theory of reliability is called a section. If you find all the sections contained in the structure and to determine their reliability, it is possible to determine the reliability of the entire structure.
In the structure shown in Fig. 1, section is formed by next set of items: 1–2, 3–4, 1–2–5, 1–3–4, 1–4–5, 2–3–4, 2–3–5, 3–4–5, 1–2–3–4, 1–2–3–5, 1–2–4–5, 2–3–4–5, 1–2–3–4–5.
The more complex the structure, the more its structure elements, the more difficult to identify them at all sections, so, to identify all sections of the structure in Fig. 1, would have to consider 32 different combinations of elements. In general, for a structure containing n elements need to consider 2n combinations. That is why the direct selection of sections of complex multiple systems are very time–consuming operation.
Among the many sections of complex structures are those which are formed by a minimal set of elements – is the minimum cross–section. For the structure shown in Figure 1 the minimum cross sections are 1–2, 3–4, 1–4–5, 2–3–4. Indeed, if in any of these kits to remove at least one element, the remaining set will not be cut (Fig. 2).
There are some groups of elements, the simultaneous failure of which leads to the rupture of all paths connecting the input and output structures. A set of elements whose failure leads to failure of the structure (ie, breaking all links between input and output) in the theory of reliability is called a section. If you find all the sections contained in the structure and to determine their reliability, it is possible to determine the reliability of the entire structure.
In the structure shown in Fig. 1, section is formed by next set of items: 1–2, 3–4, 1–2–5, 1–3–4, 1–4–5, 2–3–4, 2–3–5, 3–4–5, 1–2–3–4, 1–2–3–5, 1–2–4–5, 2–3–4–5, 1–2–3–4–5.
The more complex the structure, the more its structure elements, the more difficult to identify them at all sections, so, to identify all sections of the structure in Fig. 1, would have to consider 32 different combinations of elements. In general, for a structure containing n elements need to consider 2n combinations. That is why the direct selection of sections of complex multiple systems are very time–consuming operation.
Among the many sections of complex structures are those which are formed by a minimal set of elements – is the minimum cross–section. For the structure shown in Figure 1 the minimum cross sections are 1–2, 3–4, 1–4–5, 2–3–4. Indeed, if in any of these kits to remove at least one element, the remaining set will not be cut (Fig. 2).
In theory, the reliability of the investigations that prove the reliability of series–connected sections of minimum structure defines the lower boundary of its reliability. Moreover, the more reliable elements included in the system, the more reliable set of minimal sections reflects the reliability of the entire structure, [4].
Figure 2 – minimal cutsets
The method of decomposition of the complex structure with respect to the basic elements
Method of factorization is a second part of the algorithm.
In the complex structure of the scheme choose the basic element (or group of basic elements), usually it is the element (or group of elements) that occur in parallel branches.For such an element (or group) made the following assumptions:
a) The basic element is in working condition and is absolutely reliable;
b) The basic element is in the failed state.
For these cases, representing two mutually exclusive events, the original scheme is transformed into two new ones.
In the first scheme, the basic element is replaced by an absolutely reliable line. In the second scheme, instead of the base element – open circuit [5].
The probability of failure–free operation of the circuit consisting of n series–connected elements, or consisting of m parallel–connected elements [3]:
In the complex structure of the scheme choose the basic element (or group of basic elements), usually it is the element (or group of elements) that occur in parallel branches.For such an element (or group) made the following assumptions:
a) The basic element is in working condition and is absolutely reliable;
b) The basic element is in the failed state.
For these cases, representing two mutually exclusive events, the original scheme is transformed into two new ones.
In the first scheme, the basic element is replaced by an absolutely reliable line. In the second scheme, instead of the base element – open circuit [5].
The probability of failure–free operation of the circuit consisting of n series–connected elements, or consisting of m parallel–connected elements [3]:
where n, m – number of elements in the scheme;
pi – probability of failure of i–th element.
Our proposed algorithm is based on "the method of decomposition of the complex structure of the scheme with respect to the basic elements”, in this case, we find all possible states of the circuit, then using the method of minimal cutsets, choose those that lead to the successful functioning of the scheme.
At the Department of Electrical Systems of a Power Consumption has developed a program that allows you to use the proposed algorithm, and determine the minimum and the exact value of the probability of failure–free operation of the circuit during the time t, taking into account two types of failures: failure of the "open circuit" and the rejection of the "short circuit".
pi – probability of failure of i–th element.
Our proposed algorithm is based on "the method of decomposition of the complex structure of the scheme with respect to the basic elements”, in this case, we find all possible states of the circuit, then using the method of minimal cutsets, choose those that lead to the successful functioning of the scheme.
At the Department of Electrical Systems of a Power Consumption has developed a program that allows you to use the proposed algorithm, and determine the minimum and the exact value of the probability of failure–free operation of the circuit during the time t, taking into account two types of failures: failure of the "open circuit" and the rejection of the "short circuit".
Visual representation of the method
List of references
 |
[Resume]
Oleksiy Soleniy
| Electrotechnical Faculty |
| Department of Industrial Companies and Cities Electric Supply |
| Specialty "Electrotechnical Systems of a Power Consumption" |
| The scientific adviser: prof. Kovalev Aleksandr |
| Process optimization reliability evaluation of structural complex circuits using programming languages |
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Below is a method of expanding the complex structure of the scheme (Fig. 1) with respect to the basic elements (five elements). Element with a bar - is in working condition and is absolutely safe, with no element - is in the failed state. Using the method of minimum cross-sections (Fig. 2), choose those that lead to the successful functioning of (highlighted in blue).