In the present study, Taguchi method is used to find the optimal cutting parameters for surface roughness (Ra) in turning. The L-9 orthogonal array, the signal-to-noise ratio & analysis of variance are employed to study the performance characteristics in turning operations of Alloy Steel EN 24. The four cutting parameters namely, insert radius, depth of cut, feed & cutting speed are optimized with considerations of surface roughness. Finally, relational analysis is used to analyze the process with multi performance characteristics. The analysis of variance was used to determine the significant turning parameter that affects the performance characteristics. Lastly, the conformation test reveals the effectiveness of Grey Analysis, used to obtain the optimal combination of turning parameters. In experimental work, the feed rate is observed as most significant machining parameter with a contribution of 64%. The optimal combination of machining parameters is found for set A1, B2, C3, D3 by Grey Relational Analysis. The conformation test confirms that optimal combination determined by Grey Relational grade really provides the optimized combination of cutting parameters.