Abstract
This paper presents a techniques assessing the reliability of the complex structures which can not be reduced to a series-parallel connection of elements. In the case where the system elements can have three mutually exclusive (disjoint) states – up state, “fail-closed” mode, “fail-open” mode there is a need and an opportunity to separate the system failure probability calculations for the break and closure. It is shown that the developed method of estimating the reliability can be used for structures of any complexity with very weak restrictions. Orthogonalization are examples of logic functions based on the incompatibility of individual variables. Correctness of the proposed methods was confirmed by the decision of problems by full exhaustive search. Examples of automated modeling of bridge structure and the structure of the two stars connected to a delta solved using software ARBITR in which software is implemented algebra of mutually exclusive (disjoint) events.
Highlights
This paper presents a technique assessing the reliability of the complex structures, which can not be reduced to a series-parallel connection of elements
Automated reliability modeling procedures for structurally complex systems comprising elements with three disjoint states, implemented in the ARBITR software use the opportunities to graphically display structures in the form of two equivalent nodes and software implementation of the GDE algebra
Summary
В таблице 1 использованы следующие сокращения и обозначения: N, S, О – состояния работоспособности, отказа типа «Замыкание» или типа «Обрыв» - соответственно;. Вероятностная функция для расчета надежности параллельной системы Pc = 1 − P4 − P5 , показанная в левом нижнем углу рисунка 1, совпадает с формулой (5) при обозначениях: Rc = Pc ; Qco = P4 ; Qcз = P5 и соответствует правилу ((1.4), табл.П5.1) [4] преобразований логических и вероятностных функций для случая несовместных событий. Независимо от структуры системы, учитывая, что функция работоспособности системы (ФРС) может быть записана в виде m параллельных кратчайших путей успешного функционирования (КПУФ), а каждый КПУФ есть последовательное соединение n аргументов, можно утверждать, что, важным фактором оценки надежности систем, состоящих из элементов с тремя несовместными состояниями, является раздельное вычисление вероятностей отказов системы по «Обрыву» ( Qco ) и по.
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