Till now, in the literature, arithmetic operations between same types of vague sets are discussed. Also to analyze the fuzzy system reliability, it is assumed that the reliability of all components of a system follows the same membership function. However, in practical problems, such type of situations rarely occurs. Therefore, there is need of a method by which we can also find the fuzzy reliability of systems having components following different type of membership functions. In the present paper, a new algorithm has been introduced to perform various arithmetic operations between different types of vague sets. Further using the proposed algorithm, the methods are obtained to analyze the fuzzy reliability of various systems. Our study generalize the various work [6-8, 10-15] of the literature.