Multivariate Taguchi loss function optimization based on principal components analysis and normal boundary intersection

Optimization methods are widely used to improve industrial processes and enhance the quality characteristics of product, where process costs are directly linked. Given this assumption, this study aims to present a multivariate proposal of the Taguchi loss function, to model and optimize manufacturing processes, searching to establish values that prioritize quality and provide the minimum loss in view of the process costs. For this, design of experiments techniques will be used to model the process and the calculated loss functions. The strategy of principal components analysis is used to minimize the data dimension, considering the structure of variance–covariance. Then, the normal boundary intersection method is used to find the Pareto frontier. Based on the values, the method also proposes a total loss function equation, which is characterized as an approach to choose the optimal point based on the sum of the loss functions for the Pareto frontier through the process cost. To demonstrate the behavior of the method, the flux-cored arc welding of stainless-steel cladding process was applied. In view of the results, the method provided an optimal value at the Pareto frontier, contemplating an appropriate balance between minimal loss and higher quality, which were compared with other studies in the literature. The method also provided a reduction in computational effort of approximately 90% (from 210 to 21 subproblems), obtaining the best solution and contemplating the multivariate nature of the data.