Abstract
Problem statement. The problems of optimal structural redundancy of systems are usually formulated as a nonlinear problem of mathematical programming with integer variables, and to solve them, usually, various optimization methods are used, which requires the development of special algorithms and appropriate software. However, in the case of clarifying the original task of optimal redundancy, there is often a need to adjust the developed algorithms and software. All this greatly complicates obtaining the desired results. Another approach to solving problems of optimal redundancy of systems is the use of office information technology, the tool environment of which is adapted to solve mathematical problems, including optimization problems. This approach does not require the development of special algorithms and software. However, issues related to the effectiveness of the information technology used to solve this problem require further scientific and practical study. This article formulates a model of optimal design of redundant systems according to the criterion of minimum cost while ensuring the required level of reliability during a given time. This model is written in terms of a nonlinear problem of mathematical programming with integer variables and is numerically implemented in the operating environment of an Excel spreadsheet when the main object of the designed system consists of 6 elements. The optimal options for reserving this object according to the schemes of "hot" and "cold" redundancy are obtained. The purpose of the article is to show the effectiveness and efficiency of the MS Excel spreadsheet to solve problems of optimal structural redundancy of systems. Conclusions. This article discusses issues related to the problem of solving problems of optimal design of redundant systems in the tool environment of the MS Excel spreadsheet. Examples of solving the problems of separate "hot" and separate "cold" redundancy of a 6-element object prove the effectiveness and efficiency of the MS Excel spreadsheet to solve this problem. In addition, the developed optimization model can be successfully used in practical tasks to ensure the reliability of technical systems in the early stages of their design.
Highlights
Optimal design of redundant systems according to the criterion of minimum cost while ensuring the required level of reliability during a given time
The problems of optimal structural redundancy of systems are usually formulated as a nonlinear problem of mathematical programming
which requires the development of special algorithms
Summary
Optimal design of redundant systems according to the criterion of minimum cost while ensuring the required level of reliability during a given time. Задачі оптимального структурного резервування систем, як правило, формулюються у вигляді нелінійної задачі математичного програмування з цілочисловими змінними, а для їх розв’язання зазвичай застосовуються різноманітні методи оптимізації, що пов’язано з розробленням спеціальних алгоритмів і відповідного програмного забезпечення. Інший підхід до розв’язання задач оптимального резервування систем полягає у використанні офісних інформаційних технологій, інструментальне середовище яких адаптоване для розв’язання математичних задач, у тому числі задач оптимізації. У статті сформульовано модель оптимального проектування резервованих систем за критерієм мінімальної вартості при забезпеченні необхідного рівня надійності протягом заданого напрацювання.
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