Response Surface Methodology

Response surface methodology, or RSM, is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize the response. ... The process yield is a function of the levels ..., say

y = f(x₁,x₂) + e

where e represents the noise observed in the response y. If we denote the expected response by E(y) = f(x₁,x₂) = h, then the surface represented by

h = f(x₁,x₂)

is called the response surface.

In order to optimize competitiveness as a response, consider an objective of the form

y = a_v f_v(x) + a_c f_c(x)

where a_v is a nonnegative number, a_c is a nonpositive number, x is a vector of test variables, f_v(x) is a function of positive qualities over the test variables, and f_c(x) is a function of positive costs over the test variables. Then, maximizing y finds the most competitive set of test variables z(a_v,a_c). The numbers a_v and a_c are relative weights between qualty and cost. The trick is, of course, is to choose meaningful variables which drive quality and cost to find functions f_v(x) and f_c(x). Using response surface methodogy with an appropriate experimental design is an appropriate method of finding f_v(x) and f_c(x). Quality function deployment can be used to provide the quantities f_v and parametric cost analysis can be used to provide the quantities f_c.

Address information for a number of companies providing quality related software can be found in Struebing (1996).

References

• Montgomery, D. C. (1991). Design and Analysis of Experiments, 3rd. ed., John Wiley and Sons, New York NY.
• Struebing, L. (1996). "Quality Progress' 13th Annual QA/QC Software Directory," Quality Progress, April, pp. 31-59

Bibliographies

Response Surface Methodology

Design of Experiments

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