In experimental design, the classical Taguchi method is often used to improve processes that have only one main outcome. However, in real manufacturing, particularly during machining, it is often necessary to consider several important characteristics simultaneously. This study uses a combination of the Taguchi method and Grey Relational Analysis (GRA) to improve the CNC dry turning of Inconel 625. The goal is to make the process more efficient while also ensuring better surface quality, which are two goals that often work against each other. The approach uses data from Taguchi designs to calculate signal-to-noise ratios (S/N) and combines them with GRA to create a single measure of overall performance. To understand how each process setting affects the final result, an analysis of variance (ANOVA) is performed. The best settings found were a depth of cut of 1.0 mm, a cutting speed of 80 m/min, and a feed rate of 0.08 mm/rev. These settings give the best balance between removing material quickly and keeping the surface smooth. Tests done to examine these results confirmed that the method works well, with the actual results matching the expected outcomes closely.