Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.
The fuzzy cognitive map is considered as a tool for the ranking of factors affecting reliability. The rank of a factor is defined as an equivalent of the Birnbaum importance index in the classical reliability theory. Models and algorithms are proposed for calculation of the importance indexes of single factors and their joint effects on the reliability. The method is exemplified by the reliability and safety of an automobile in the “driver-automobile-road” system subject to the driver's qualification, traffic situation, unit costs of operation, operating conditions, maintenance scheduling, quality of maintenance and repair, quality of automobile design, quality of operational materials and spare parts, as well as storage conditions. The advantages of the method include 1) use of available expert information with no collection and processing statistical data and 2) capability to take into account any quantitative and qualitative factors associated with people, technology, software, quality of service, operating conditions, etc.
In this paper, we propose a method for analyzing a catastrophe tree that is an analog of the classical method for analyzing a fault tree, which does not require knowledge of the probabilities of events. The concept of the possibility of bifurcation, which is estimated by a number in the interval [0,1] using catastrophe theory and corresponds to the membership function of a fuzzy set, is used instead of the concept of the probability of failure. The possibility of bifurcation (or catastrophe) of the system is calculated using specially introduced rules for aggregating the possibilities of bifurcations for various logical operations of the fault tree. The catastrophe analysis method is illustrated using the example of a fault tree for a road accident at a T-junction.
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