| Reliability theory is a synthesis and margin subject to study the character of the life of the product, and it involves the fundamental science, the technology and management science.The reliability mathematics is one of the fundamental reliability theory, and has turned into the boundary embranchment science of applied probability, of applied mathematical statistics and of operational research. Reliability mathematics carries through the reliability researches of system almost suppose that parts are in the condition of independence, but do not deal with the case of dependent. So, in this paper, conneted function Copula is applied to study the reliability of depedent parts.Copula is the function with many excellent properties that couples the joint distribution function of random variables to its univariate margins, and is a all-right tool to investigate the dependence properties. On the base of reliability mathematics, this paper will study the reliability index of system consisted of dependent parts and break through the limit of independence. The distribution functions of life of each parts interprets the each characteristic, but Copula interprets the characteristic of system and the effect which dependent parts make to system.This paper will mostly study several simple systems, (series system, parallel connection system, series-parallel connection system, vote system and cold store system, etc.) and how to show the dependent relation of each parts with Copula. The change relation of the reliability measure and Copula of dependent parts is studied in series system and parallel connection system and series-parallel connection system. The difference of the reliability between the dependence and independence parts is made, and the partecular family of positive (or negative) dependent Copula is how to be made. Because the combination form of parts in each system is different, the form of Copula which interprets the dependent relation of each parts in system is not the same.
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