Comparing DEA and principal component analysis in the multiobjective optimization of P-GMAW process

The optimization of a multiresponse manufacturing process is not a trivial task. Many authors have tried to overcome the particular difficulties observed in this knowledge area exploring the powerful mechanisms present in a great deal of techniques like design of experiments, response surface methodology (RSM), principal component analysis (PCA) and mathematical programming. In this sense, this paper presents an alternative hybrid approach, combining RSM and data envelopment analysis (DEA), a popular linear programming technique useful to compare efficiency of decision making units. The basic idea is to optimize a set of multiple correlated responses of a well-defined manufacturing process using DEA as an algorithm for generated the singular objective function. This alternative proposal is compared to multivariate response surface methodology, a stochastic approach based on the PCA, a multivariate statistical technique usually employed with Taguchi multiresponse designs. Since a great number of manufacturing processes present sets of multiple correlated responses, a case study based in a five quality characteristics of a pulsed GMAW welding process is here presented to illustrate the comparative performance of two proposals. The results indicate close responses for both methods. In spite of this, DEA was considered better because its results are larger in parameters that we wanted maximize and are smaller in parameters we wanted minimize. All established constraints were not violated in both cases of DEA.