Page 176 - Six Sigma Demystified

Chapter 7 i m p r o v e S tag e 157

prove stage, these process drivers will be investigated further to define the set-
tings necessary to achieve optimal process performance.
There are two aspects, or objectives, of optimization. Traditionally, optimiza-
tion involves finding the best combination of factor levels to maximize (or
minimize) the response. For example, it may be important to investigate the
specific concentrations of reagents and temperature of reaction necessary to
achieve the highest degree of product purity. In a service process, the optimal
allocation of staffing and services may be needed to minimize the cycle time
for a key process.
More recently, perhaps owing to the influence of Taguchi, there is an
increased interest in variation reduction. In this scope, optimization leads to the
best combination of factor levels to produce the least variation in the response
at a satisfactory average response. For example, the chemical process customer
may be most interested in a consistent purity level. This is often the case when
customers can make adjustments to their process over the long term, but
short- term adjustments to deal with batch- to- batch variation are costly. This
happens in service processes as well. An oil- change service that provides a con-
sistent two- hour service is often preferred to one that occasionally delivers with
half- hour service but sometimes makes the customer wait several hours. Con-
sistency enhances the ability to plan, which improves resource utilization.
Inconsistency mandates complexity, which comes at a cost, as is often discov-
ered in the earlier stages of DMAIC.
When optimal solutions to problems are sought and the process model is not
clearly understood, the response surface methods generally are the most useful.
Response surface designs are special- case- designed experiments that allow opti-
mal regions to be located efficiently with usually only a few iterations. The

first- order regression model developed in the analyze stage serves as the starting
point. This first- order model is a good assumption because the starting point is
usually far enough away from the optimum that it is likely to be dominated by
first- order effects, and a detailed mapping of the response region far away from
the optimum is not needed. Data are collected through experimentation to
determine the path toward optimality using the first- order model. Tests for
curvature indicate when a local minimum, maximum, or saddle point (a com-
bination of the two) is reached.
Using three- or five- evel central composite designs, the response surface can
l
be mapped using a higher- order model. Although response surface plots such as
the one shown in Figure 7.2 are visually appealing, the classic contour plot (such
as the one shown in Figure 7.3) is often more useful because of its direct approach.