An investigation on the use of response surface methods for process improvement

ABSTRACT Response surface methodology is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which a response of interest is influenced by several input variables and the objective is to optimize this response. The techniques used in response surface methodology include the following: 1. Designing a set of experiments that will yield adequate and reliable measurements of the response of interest, 2. Determining a model that best fits the data collected from the design chosen in (1), and 3. Determining the optimal settings of experimental factors that produce optimum value of the response. In this study, the techniques used in response surface methodology are presented: Experimental designs that are set up for the purpose of collecting data for fitting first- order second-order models are presented. Techniques for the determination of optimum conditions when a first-order or a second-order model is fitted to a data set are given (steepest ascent, canonical analysis, and ridge analysis). It is devoted to a discussion of some multivariate aspects of response surface methodology with regard to parameter estimation, lack of fit, and simultaneous optimization. Dual response techniques, desirability function approach, and generalized distance approach are presented. Another distance function, particularly to those who like consider relative changes from the individual optimum, is proposed. Response surface alternatives to the Genichi Taguchi's robust parameter design approach are presented. It has also been shown how desirability function approach, generalized distance approach, and relative distance approach can be applied in robust design studies. When there are several responses, multivariate expected loss function can be used for achieving a robust process. Several examples illustrate these procedures are given in the application chapter.