Formal Solution of N-Type Robust Parameter Design Problems with Stochastic Noise Factors

The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The design obtained is robust in that the sensitivity to variations of uncontrollable factors (noise) has been minimized. The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven even for problems where the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be used, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multiparametric case must take into account the characteristics of the probability space on which the random parameters are defined.