ABSTRACT
Mathematical representation of investigated system is important step of reliability analysis. There are two principal representations of considered system. The first one is known as Binary-State System (BSS), and it permits considering only two states in system/components performance— functioning and failed. Very often, this is not sufficient to adequate mathematical description of system behavior. Therefore, other types of mathematical representation are used. Multi-State System (MSS) is one of most prospective mathematical representations. This representation allows defining more than two states in describing behavior of the system and its components. A MSS can be described by structure function, which defines unambiguous correlation between all possible combinations of states of the system components and the system state. Typical disadvantages of MSS are large dimension and impossibility to form structure function based on uncertain data. We propose to consider application of mathematical methods of Multiple-Valued Logic (MVL) to form the MSS structure function. MVL is natural extension of Boolean algebra in MSS reliability assessment. This logic has been used for analysis of logic functions with more than two values. New method for structure function forming based on uncertain data and application of MVL methods is proposed. Multi-Valued Decision Diagrams (MDDs) are used for structure function representation, in particular. A MDD is useful data structure for representation of MVL function of large dimension. The method presented in this paper takes into account two disadvantages of MSS representation by structure function.
