In off-line quality control the method is either to check the quality of few products from a batch or lot (acceptance sampling) or to evaluate the best process environment capable of producing desired quality product. This invites optimization problem which seeks identification of the best process condition or parametric combination for the said manufacturing process. If more than one attribute comes into consideration it is very difficult to select the optimal setting which can achieve all quality requirements simultaneously. Otherwise optimizing one quality feature may lead severe quality loss to other quality characteristics which may not be accepted by the customers. In order to tackle such a multi-objective optimization problem, the present work applied extended Taguchi method with Grey Relational Analysis. This work aimed at evaluating the best process environment which could simultaneously satisfy requirements of both quality and as well as productivity. This work should be especially useful to both faculty as well as students of post-graduation in Mechanical (manufacturing) engineering.