Fuzzy Reliability Analysis Of General Series And Parallel System

Fuzzy Theory is based on the phenomenon that there is not a clear boundary ofsome concepts and collections, such as tall and short, big and small. Later it is furtherdeveloped into the Fuzzy Reliability Theory which can be regarded as an expansion anddevelopment of the Classical Reliability Theory.At the very beginning, main points and achievements of three Fuzzy reliabilitytheories are summarized and analyzed. This paper mainly focuses on the detaileddescription and further research of Posbist fuzzy reliability theory.With analyses of fuzzy variables and fuzzy events, the relationship between theindependence of fuzzy variables and that of fuzzy events is clarified. Then this paperderives the membership function of general series system and Posbist fuzzy reliabilityas well as Posbist fuzzy unreliability of general parallel system and its correspondingmembership function.Main tasks and results are as follows:①Make a brief introduction of basic concepts and properties of fuzzy set and fuzzynumber.②Conduct a detailed summary and analysis of the Probist Fuzzy Reliability Theoryand FuzzyEvent Theory. Then derive calculation formulas of reliability indexes of seriessystem and parallel system based on these two theoretical frameworks, and someexamples are given.③Introduce in detail the structure and theoretical foundation of the Posbist fuzzyreliability theory. Then the membership function and Posbist fuzzy reliability ofseries system with two components are analyzed and discussed. So does that ofparallel system.④Under the theoretical framework of Posbist fuzzy reliability, discuss and prove therelationship between independence of fuzzy variables and independence of fuzzyevents. On this basis, give the Posbist fuzzy reliability of multi-unit series systemand its corresponding membership function. At the same time, discuss the Posbistfuzzy unreliability of general parallel system and derive its membership functionand also formulas of Posbist fuzzy unreliability.This is the main innovation of thispaper as well as an important step forward in the development of the Posbist fuzzy reliability theory.