Algebra of algorithms and fuzzy logic in system reliability analysis

Abstract

A method for simulating system reliability based on the algebra of regular algorithms and fuzzy set theory is proposed. The reliability model is supported by a logic-algorithmic description of events associated with faults (failures and errors) occurred, detected and removed while the system is executing the task. The initial data for the simulation are membership functions and fuzzy IF-THEN rules that characterize whether the operator and logical elements of the model are executed correctly depending on the measurable parameters and influencing factors. Contraction-extension operations for membership functions help take into account the quality of checking and correction procedures. The result of application of the method is a multidimensional membership function that gives the distribution of correctness of task execution, depending on the parameters of objects and processes that compose the system. A fuzzy algorithmic algebra that represents formal rules of transition from operations in the algebra of regular algorithms to the corresponding operations over membership functions of operators and conditions is developed to implement the method.