FORMAL SOLUTION OF N-TYPE ROBUST PARAMETER DESIGN-PROBLEMS WITH STOCHASTIC NOISE FACTORS

The Taguchi method of product design is a statistical experimental tec hnique aimed at reducing the variance of a product performance charact eristic due to uncontrollable factors. The goal of this paper is to pr ovide a monotonicity analysis based methodology to facilitate the solu tion of N-type parameter design problems. The design obtained is robus t in that the sensitivity to variations of uncontrollable factors (noi se) has been minimized. The performance characteristic is unbiased in the sense that its expected value equals a target or specification. Th e proposed loss function is based on the absolute deviation of the cha racteristic with respect to the target, instead of the common square e rror approach. Conditions, like those imposed by monotonicity analysis , on the monotonic characteristics of the performance function are pro ven even for problems where the objective function is not monotonic an d contains stochastic parameters. These conditions allow the qualitati ve analysis of the problem to identify the activity of some constraint s. Identification of active sets of constraints allows a problem reduc tion strategy to be used, where the solution to the original problem i s 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 mu ltiparametric case must take into account the characteristics of the p robability space on which the random parameters are defined.