A normal boundary intersection approach to multiresponse robust optimization of the surface roughness in end milling process with combined arrays

Robust parameter design (RPD) has recently been applied in modern industries in a large deal of processes. This technique is occasionally employed as a multiobjective optimization approach using weighted sums as a trade-off strategy; in such cases, however, a considerable number of gaps have arisen. In this paper, the use of normal boundary intersection (NBI) method coupled with mean-squared error (MSE) functions is proposed. This approach is capable of generating equispaced Pareto frontiers for a bi-objective robust design model, independent of the relative scales of the objective functions. To verify the adequacy of this proposal, a central composite design (CCD) is developed with combined arrays for the AISI 1045 steel end milling process. In this case study, a CCD with three noise factors and four control factors are used to create the mean and variance equations for MSE of two quality characteristics. The numerical results indicate the NBI-MSE approach is capable of generating a convex and equispaced Pareto frontier to MSE functions of surface roughness, thus nullifying the drawbacks of weighted sums. Moreover, the results show that the achieved optimum lessens the sensitivity of the end milling process to the variability transmitted by the noise factors.