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The objective of this investigational analysis was to study the influence of process variables on the response during the drilling of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>LM</mi><mn>6</mn><mo>/</mo><msub><mi mathvariant="normal">B</mi><mn>4</mn></msub><mi mathvariant="normal">C</mi></mrow></semantics></math></inline-formula> composite materials. Stir casting was employed to produce the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>LM</mi><mn>6</mn><mo>/</mo><msub><mi mathvariant="normal">B</mi><mn>4</mn></msub><mi mathvariant="normal">C</mi></mrow></semantics></math></inline-formula> composites. A Vertical Machining Center (VMC) with a dynamometer was used to drill the holes and to record the thrust force. An L27 orthogonal array was used to carry out the experimental work. A grey relational analysis (GRA) was employed to perform optimization in order to attain the lowest Thrust Force (TF), Surface Roughness (SR) and Burr Height (BH). For minimal responses, the optimum levels of the process variables viz. the feed rate (F), spindle speed (S), drill material (D) and reinforcing percentage (R) were determined. The process variables in the drilling of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>LM</mi><mn>6</mn><mo>/</mo><msub><mi mathvariant="normal">B</mi><mn>4</mn></msub><mi mathvariant="normal">C</mi></mrow></semantics></math></inline-formula> composites were indeed optimized, according to confirmational investigations. The predicted Grey Relational Grade was 0.846, whereas the experimental GRG was 0.865, with a 2.2% error—indicating that the optimization process was valid.