Magnesium and its alloys reinforced with nano-size reinforcements have attracted the interest of the researchers because of its high strength to weight ratio, high damping capacity and displays improved mechanical property without affecting the ductility.The light weight nature of this structural material makes them a right choice to be used in the automobile and aerospace sector where weight reduction is a primary concern.This work determines optimum process parameters such as pulse on time, pulse off time, peak current, servo voltage and volume of silicon carbide (SiC p ) percentage which influence the wire electro discharge machining (WEDM) process during machining of AZ31B magnesium alloy based metal matrix nano-composite (MMNC) using combined methods of response surface methodology (RSM) and Taguchi-GRA-PCA hybrid method.Taguchi L27 experimental design is used in the experimental investigation, and a predictive model is developed to identify the optimum process parameters in the micro EDM process, which influence two main machining criterions such as surface roughness (SR) and material removal rate (MRR).Further analysis of variance (ANOVA) is carried out to determine the adequacy of the model and to identify which parameters has most influence on the responses.The proposed method can be used to select optimal process parameters from various sets of combinations of process parameters in a WEDM process.