Plateau surfaces have excellent sliding properties, because only the high peaks of surface asperity are smoothed. Therefore, they form the sliding surfaces of automobile engines and machine tools, contributing to their high performance and low environmental impact. As the development and production of these machines require the evaluation of their plateau surface components, methods for plateau surface evaluation have been proposed by the International Organization for Standardization (ISO) and previous researches. These evaluation methods include a processing procedure for fitting a hyperbola to the material probability curve (MPC) of the plateau surface. However, the ISO standard does not clearly state the rationale for restricting the fitting curve to a hyperbola. As shown in a previous study, another curve that can fit the shape of the MPC of the plateau surface is expected to be a parabola in addition to a hyperbola. The parabola and hyperbola are curves known as conic sections
. In this research, we examine the validity of hyperbolic curve fitting and explore the fitting of conic curve by utilizing the information of conjugate diameters. Approximations using a curve better suited to the shape of the MPCs of the plateau surface can anticipate to the realization of higher quality evaluations of the surface. Through this research, we aim to contribute to the development of industry as well as improve the performance and environmental impact of automobile engines and machine tools.