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In reliability theory, some measures are introduced , called importance measures, to evaluate the relative importance
of individual components or groups of components in a system. Importance measures are quantitive criteria
that ranke the components according to their importance. In the literature, different importance measures are presented
based on different scenarios. These measures can be determined based on the system structure, reliability of
the components and/or component liftime distributions. The purpose of this paper is the study different importance
measures of the components of a system in reliability theory.

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Copula functions are  useful tools in modeling the dependence between random variables, but most existing copula functions are symmetric, while in many applications, asymmetric joint functions are required. One of these applications is reliability modeling, where asymmetric joint functions can explain different tail dependencies and provide a better model. Therefore, the theory of constructing asymmetric copula functions that can model a wider range of data has been developed. In this research, while reviewing the methods of creating asymmetric copula functions that can provide various tail dependencies, these functions are used to estimate the two-dimensional reliability of data on the age an usage of Rana and Dana cars.