A reliable system means being able to perform its intended functions. Therefore, ensuring performing of its required functions will help to enhance its reliability. For a manufacturing system (e.g. computer numerical control machines), there are a large number of functions, which complicate and make analysis difficult. In this article, a logical and systems approach of graph theory, which is effective to eliminate such difficulties, is employed. The graph theoretic models do consider the system structure explicitly and are applied to model functions at various hierarchical levels of a manufacturing system. These function digraph models are analysed using matrix approach to examine the cause and effect, which helps to evaluate importance of the function and hence provide direction for system reliability enhancement. A step-by-step methodology is presented, which is illustrated by an example of manufacturing system: computer numerical control drilling machine.