Since a fine ceramic is possessed of creditable physical and chemical material properties: high thermal resistance, chemical inertness and frictional wear resistance, its applications have been increasing in various industrial fields. Yttria(Y2O3) ceramic, which is formed of cubic crystal structure, has been considered as a light-transmitting material for an optical application and suitable buffer layer in the electronic industry. And its other applications have been increasing recently. For the effective applications of Yttria ceramic, it needs to improve a surface characteristic such as the waviness and surface roughness. The lapping process with in-process electrolytic dressing(IED) method has been performed in the surface machining of high hard-brittle material. IED method is able to overcome the surface machining defects caused by worn grains and unstable chip discharge during conventional lapping process. However, the machining control should be carefully conducted and investigated about each material because its material properties are different each other and exceedingly sensitive. Taguchi method, called robust design, is a useful method for engineering productivity elevation. It is able to search a powerful factor, which influences optimal process design, in accordance with considering noise factors reduction. When diverse factors influence a result according to complex actions each other, it needs to search optimal condition of factors. Response surface design has been widely used in various industrial fields. It helps to solve process design problems in accordance with robust design of process condition.