Nowadays, competition in various industries focuses on reducing production waste and improving the quality of manufactured products. In this article, the improvement of surface roughness quality of AISI 4340 workpieces in the turning process using TiN-coated carbide tools is investigated. For this purpose, the parameters affecting the surface quality, namely cutting speed, feed rate, and depth of cut, were selected as the input factors for the experiments. Then, the degrees of freedom of the system and the required number of levels were determined, and the corresponding orthogonal arrays were calculated. Accordingly, twenty-seven experiments were designed to measure the surface roughness values, and for each experiment, three measurements of the surface roughness parameter were recorded. Next, by calculating the grey ratios, grey coefficients, and grey grades using the relevant formulas, the final grey relational graphs were plotted for all three levels of the experiments. Based on the grey relational diagram, the percentage influence of each input parameter on achieving the desired surface roughness was determined, and the optimal numerical values for these parameters were identified. A comparison of the grey analysis results with the actual experimental data confirms the accuracy and capability of this method in predicting surface roughness in the turning process.