An internal lobe pump is suitable for oil hydraulics of machine tools, automotive engines, compressors, constructions and other various applications. In particular, the pump is an essential machine element of an automotive engine to feed lubricant oil. The subject of this paper is the theoretical analysis of internal lobe pump whose the main components are the rotors: usually the outer one is characterized by lobe with multiple profile(ellipse1, involute and ellipse2) shapes, while the inner rotor profile is determined as conjugate to the other. Also, the design of outer rotor depends on new applications with removing carryover phenomenon. The system generates new lobe profile and calculates automatically the flow rate and flow rate irregularity according to the lobe profile generated. In order to obtain rotor shapes in performance and to find optimize the design parameters, a Taguchi method is proposed in this paper. Results obtained from the analysis enable the designer and manufacturer of oil pump to be more efficient in this field.