A Construction Method Of The System Construction Function

Copulas are widely paid attention in recent years as a method which describe dependence of random variables. Its emerge makes the description of dependence between random variables perfect .But copulas can use not only in probability, statistics, and stochastic processes, but also in many other fields .In this paper, the author applies copula theory into system theory.Systematic construction function is an important notion. It is a function that links systematic condition and component condition. In the reliability theory, the definitions of construction function and dual construction function are given on the basis of systematic condition, and the two conditions, including normal and invalid, are considered. Evidently, two different components are in the same condition when they are working. However, their reliability and accumulated invalid rate of systems must not be equal, so this definition does not offer those measures that indicate the systems, such as reliability and accumulated invalid rate of systems with fine explanation. In order to describe the systematic condition in different time, we need a new method to study the systematic construction function.So, the paper gives another definition of systematic construction function from accumulated invalid rate of systems. If the system is different, so is the link way. This paper gives a specific link fashion to study some characters of those systems that are constructed by this specific construction function. In addition, this paper gives the definition of the dual system. This definition can be used in the condition of independence and dependence. When the component isdependent, this definition can not only give the according dual construction style, but also depict the dependence among the components.