Research, Basic System Reliability Based On The Copula Function

With the development of technology, people have developed a number of large and complex equipments and systems, such as in the aerospace field etc. The common features of these systems are structurally complex and powerful. The more complex the system, the more prone to failure. To a degree of the complexity seriously impacts the reliability of system, the system complexity will lost its meaning. The sharp contradictions can be seen between complexity and reliability. But the actual need that the system must have a specific function, which means that the system has a certain degree of complexity. So there is a practical study of the system reliability indexes as a way to set a more reasonable reliability of the system, which is a very important guiding significance for improving the reliability of system.Reliability theory is a synthesis and margin subject to study the character of the life of the product, and it is one of the important tools to study the reliability of system. Its defect lies in that it always supposes that parts of system are in the condition of independence when it is applied to study the reliability of system, but do not deal with the case of dependent. In addition to the study of the dependence of parts is very complex, but important thing is that there is not the very powerful tool to describe the dependence. The appearance of Copula function provides a very powerful tool for the study of reliability of system consisted of part dependence components. In view of the defects when people study the reliability of system using reliability theory, as well as the practical requires high reliabilities, this paper will explore the reliability indexes of system consisted of part dependence components.Copula function is also known as link function, which is characterized by the joint distribution of random variables connected with the marginal distributions, with some good character and unique advantages. In this paper, we apply Copula function to study the reliability of system consisted of part dependence components, which not only breaks through the case in which people only study the reliability of system consisted of completely independent components using reliability theory, but also breaks through the case in which partial scholars only study the reliability of system consisted of completely dependent components basing on Copula theory. The study in this paper reflects the universal of reality. This paper will mostly explore simple systems which include series system,parallel connection system series,series-parallel connection system,parallel-series connection system, and study how to describe reliability indexes with the "uniformierung" format, and get expressions of reliability,failure rate and mean time to failure(MTTF) using Copula function. At the same time we also give the corresponding numerical examples for each system.