This paper presents an application of interactive fuzzy goal programming to the nonlinear multi-objective reliability optimization problem considering system reliability and cost of the system as objective functions. As the decision maker always have an intention to produce highly reliable system with minimum cost, therefore, we introduce the interactive method to design a high productivity system here. This method plays an important role to maximize the worst lower bound to obtain the preferred compromise solution which is close to the best upper bound of each objective functions. Until the preferred compromise solution is reached, new lower bounds corresponding to each objective functions will be determined based on the present solution to develop the updated membership functions as well as aspiration levels to resolve the proposed problem. Considering judgmental vagueness of decision maker, here we consider the resources as trapezoidal fuzzy numbers and apply total integral value of fuzzy number to transform into crisp one. To illustrate the methodology and performance of this approach, numerical examples are presented and evaluated by comparing with the other method at the end of this paper.