Research On Reliability Of Multi - State String And Parallel Dependent System Based On Copula

With the development of science and technology, modern systems and equipment is becoming more and more complex, precision demand is higher and higher, it was found that multiple states occur during the failure process of systems and components. Thus the reliability study about multi-state systems is becoming more and more important. In the traditional reliability study, we always assume that components are independent of each other, but in real life they are not independent of each other because of common random environment and same load and pressure, they more or less have a certain correlation.As a kind function that connect the joint distribution function with their marginal function, it is an important and very effective way to solve multivariate joint distribution function of dependent random variables from different marginal distribution. Copulas function theory also provides a way isolating the marginal distribution from dependent structure, thus the study of multivariate dependence structure translates into the research of multiple distribution function. What’s more, it not only can describe linear correlation between variables, but also can deal with nonlinear dependency relationship between variables. And copulas function keep invariance under strictly increasing transformation of random variables. That is to say, the development of copulas function theory provides a new research method about dependent system.In combination with the theory of multi-state system and copulas function theory, this article calculated the reliability index about safety-critical system and multi-state dependent system consist of components with three-states. For safety-critical system, we derived the reliability index of unit safety-critical system, two units series safety-critical system, two units parallel safety-critical system. Through the reasonable mathematical modeling, we obtained the mathematical formula of probability of work and failure of safety probability, failure of danger probability, average time of failure of safety, average time of failure of danger and gave a numerical example. For simple structure multi-state dependent system, we first gave the definition of multi-state system and the assessment of multi-state component state probability and derived the reliability index of the series system and parallel system that composed of two types of failure components or three state deterioration components. And we also contrast their reliability based on some certain conditions and gave a numerical example.In all, this article applied copulas function to analyze the reliability about multi-state dependent system on series and parallel structure, it has certain theoretical value for the development of the theory of multi-state system.