Fuzzy cognitive maps in the dependability analysis of systems

Aim. Dependability simulation of a complex system starts with its structuring, i.e. partitioning into components (blocks, units, elements), for which probabilities of failure are known. The classical dependability theory uses the concept of structural function that allows ranking elements by their importance, which is required for optimal distribution of the resources allocated to ensuring system dependability. Man-machine systems are structured using an algorithmic description of discrete processes of operation, where the presence of clear boundaries between individual operations allows collecting statistical data on the probabilities of error that is required for modeling. Algorithmization is complicated in case of man-machine systems with continuous human activity, where the absence of clear boundaries between operations prevents the correct assessment of the probability of their correct performance. For that reason, the process of operation has to be considered as a single operation, whose correct performance depends on heterogeneous and interconnected human-machine system-related, technical, software-specific, managerial and other factors. The simulated system becomes a “black box” with unknown structure (output is dependability, inputs are contributing factors), while the problem of element ranking typical to the dependability theory comes down to the problem of factor ranking. Regression analysis is one of the most popular means of multifactor dependability simulation of man-machine systems. It requires a large quantity of experimental data and is not compatible with qualitative factors that are measured by expert methods. The “if – then” fuzzy rule is a convenient tool for expert information processing. However, regression analysis and fuzzy rules have a common limitation: they require independent input variables, i.e. contributing factors. Fuzzy cognitive maps do not have this restriction. They are a new simulation tool that is not yet widely used in the dependability theory. The Aim of the paper is to raise awareness of dependability simulation with fuzzy cognitive maps.

Method. It is proposed – based on the theory of fuzzy cognitive maps – to rank factors that affect system dependability. The method is based on the formalization of causal relationships between the contributing factors and the dependability in the form of a fuzzy cognitive map, i.e. directed graph, whose node correspond to the system’s dependability and contributing factors, while the weighted edges indicate the magnitude of the factors’ effect on each other and the system’s dependability. The rank of a factor is defined as an equivalent of the element’s importance index per Birnbaum, which, in the probabilistic dependability theory is calculated based on the structure function.

Results. Models and algorithms are proposed for calculation of the importance indexes of single factors and respective effects that affect system dependability represented with a fuzzy cognitive map. The method is exemplified by the dependability 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.

Conclusions. The advantages of the method include: a) use of available expert information with no collection and processing statistical data; b) capability to take into account any quantitative and qualitative factors associated with people, technology, software, quality of service, operating conditions, etc.; c) ease of expansion of the number of considered factors through the introduction of additional nodes and edges of the cognitive map graph. The method can be applied to complex systems with fuzzy structures, whose dependability strongly depends on interrelated factors that are measured by means of expert methods.

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