Abstract
The purpose of this paper is to propose a computational technique for evaluating the reliability of networks subject to stochastic failures. In this computation, a mathematical model is provided using a technique which incorporates the effect of the factoring decomposition theorem using polygon-to-chain and series-parallel reductions. The algorithm proceeds by identifying iteratively one of seven polygons and when it is discovered, the polygon is immediately removed and replaced by a simple chain after having changed the individual values of the reliability of each edge and each node of the polygon. Theoretically, the mathematical development follows the results presented by Satyanarayana & Wood and Theologou & Carlier. The computation process is recursively performed and less constrained in term of execution time and memory space, and generates an exact value of the reliability.
Highlights
Over the last decades, the reliability evaluation of systems and networks has become a priority for all manufacturers, in areas when human life is at stake
The purpose of this paper is to propose a computational technique for evaluating the reliability of networks subject to stochastic failures
The reliability evaluation of systems and networks has become a priority for all manufacturers, in areas when human life is at stake
Summary
The reliability evaluation of systems and networks has become a priority for all manufacturers, in areas when human life is at stake. The problem of evaluating the reliability of networks has been verified to be NP-hard [28] and to be a counting problem or #-P-complete (number P-complete) problem ([28] [29] [30]) To avoid such complexity, several methods and techniques have been proposed, such as factoring and reductions algorithms. Almost in the same time other researchers proposed a new category of methods which combines the factoring theorem and reduction operations using an efficient procedure that transforms a polygon structure into a simple chain and from which it becomes very easy to determine the reliability [2] [15] [16] [21] [23] [30] [33] [34] [35].
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