AN OVERVIEW OF RESPONSE SURFACE METHODOLOGY

The strategy for robust design experiments that will be considered in Section 2.3 is based on the statistical techniques associated with response surface methodology. This section will give an overview of response surface methodology, presenting some of the more common experimental designs that have been developed in this area. 

To motivate the response surface approach, suppose that there is some response of interest (for example, crushing strength in the tablet formulation example of Section 2.1.1), and a set of quantitative, continuous design variables that are of interest to the researcher (for example, the quantities of glidant, lactose, and disintegrant for the tablet formulation example). One possible objective for the researcher might be to understand and describe the relationship between the design variables and the response. This relationship can be described mathematically by 

To introduce some notation, let the response of interest be denoted by t] and suppose that there are p quantitative, continuous design variables, x,  

In response surface methodology, it is frequently assumed that / can be approximated in some region of the design variables by a low-degree polynomial. For example, if p=2, and a first-order model is assumed appropriate then 

Alternatively, the experimenter might assume that / can be approximated by a second-order model so that 

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