ВВЕДЕНИЕ. По структурной схеме надежности технической системы (все элементы системы работают в режиме нормальной эксплуатации – простейший поток отказов) в соответствии

По структурной схеме надежности технической системы (все элементы системы работают в режиме нормальной эксплуатации – простейший поток отказов) в соответствии с вариантом задания, требуемому значению вероятности безотказной работы системы и значениям интенсивностей отказов ее элементов требуется определить:

– функцию алгебры логики y(x) с помощью дерева отказов;

– функцию надёжности h(r) с помощью алгоритмов разрезания или ортогонализации;

– построить график изменения вероятности безотказной работы системы от времени наработкив диапазоне снижения вероятности до уровня 0.1 - 0.2;

– определить - процентную наработку технической системы;

– элементы, имеющие наименьшие значения надёжности;

– элементы, являющиеся критичными для системы.

Исходные данные для расчетов представлены в таблице 1.

Таблица 1 – Исходныеданные

1 ОПРЕДЕЛЕНИЕ ФУНКЦИИ АЛГЕБРЫ ЛОГИКИ

Структурная схема надежности системы представлена на рисунке 1.

Рисунок 1 – Структурная схема надежности

Объединим элементы, которые соединены последовательно или параллельно, в группы. На первом этапе получим: A = {2, 7}; B = {6, 11, 16}; C = {12, 17}; D = {8, 13, 18}; E = {4, 9, 14}; F = {5, 10, 15}; G= {19, 20}.

Таким образом, структурная схема примет следующий вид:

Рисунок 2 – Структурная схема надежности

На втором этапе получаем X = {1, A, 3, E, F}; Y = {B, C, D, G}. Структурная схема надежности на этом этапе показана на рисунке 3.

Рисунок 3 – Структурная схема надежности

Занесем события на схему дерева отказов, представленную на рисунке 4.

Рисунок 4 – Дерево отказов

Составим функцию алгебры логики.

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2 ОПРЕДЕЛЕНИЕ ФУНКЦИИ НАДЕЖНОСТИ

Для перехода от функции алгебры логики к вероятностной функции можно воспользоваться алгоритмом ортогонализации.

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