Adaptive network based fuzzy inference system (ANFIS) is an intelligent neuro-fuzzy technique used for modeling and control of ill-defined and uncertain systems. ANFIS is based on the input-output data pairs of the system under consideration. The size of the input-output data set is very crucial when the data available is very less and the generation of data is a costly affair. Under such circumstances, optimization in the number of data used for learning is of prime concern. In this paper we have proposed an ANFIS based system modeling where the number of data pairs employed for training is minimized by application of an engineering statistical technique called full factorial design. Our proposed method is experimentally validated by applying it to the benchmark Box and Jenkins gas furnace data. By employing our proposed method the number of data required for learning in the ANFIS network could be significantly reduced and thereby computation time as well as computation complexity is remarkably reduced. The results obtained by applying our proposed method are compared with those obtained by using conventional ANFIS network. It was found that our model compares favorably well with conventional ANFIS model.