In conventional reliability analysis, the failure probabilities of the components of a system are treated as exact values. It is often difficult to obtain data for failure probabilities under changing environmental conditions. Hence fuzzy sets are used to analyze the fuzzy system reliability, where a fuzzy number represents the reliability of each component. Chen [14] analyzed the fuzzy system reliability using vague set theory. The values of the membership and non-membership of an element, in a vague set, are represented by a real number in [0, 1]. A specialist is always uncertain about the values of the membership and non-membership of an element in a set. Hence, it is better to represent the values of the membership and non-membership of an element in a set by intervals of possible real numbers instead of real numbers. In this paper a new method has been developed for analyzing the fuzzy system reliability of a series and parallel system using interval valued trapezoidal vague sets, where the reliability of each component of each system is represented by an interval valued trapezoidal vague set defined in the universe of discourse [0, 1].The developed method has been used to analyze the fuzzy reliability of a marine power plant. The major advantage of the proposed approach (the concept of interval valued vague sets) over the existing approaches [7, 8, 14] is that the proposed approach separates the positive and negative evidence for the membership of an element in a set. Also in the proposed approach the values of the membership and non- membership of an element in a set are intervals instead of a single real number.