The use of an internal lobe pump is suitable for enhancing the oil hydraulics of machine tools, automotive engines, compressors, constructions and various other applications. In particular, the pump is an essential machine element for supplying lubricants in an automotive engine. The subject of this paper is the theoretical analysis of an internal lobe pump whose main components are inner and outer rotors; the outer rotor is characterized by a lobe with multiple profile shapes (ellipse 1, involute, and ellipse 2), while the profile of the inner rotor is determined as a function of the profile of the outer rotor. Further, the design of the outer rotor depends on new applications and it eliminates the carryover phenomenon. The system suggested in this study generates a new lobe profile and automatically calculates the flow rate and flow rate irregularity according to the generated lobe profile. In this study, the Taguchi method is used to determine the optimal rotor shapes and design parameters of the pump performance. The results obtained by the analysis enable the designer and manufacturer of oil pumps to achieve higher efficiency.