Page 381 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 361

concentrations of reagents and temperature of a reaction to achieve the highest
degree of product purity. In a service process, we may seek optimal allocation
of staffing and services to minimize the cycle time for a key process.

When to Use

Improve Stage

• To map the response surface in the region of interest to provide a predic-
tion of the change in the response as factor settings vary
• To optimize the response, such as a maximum or minimum response or
minimum variation in the response, to achieve improved process capabil-
ity and yield for existing processes or best performance for new products
or processes

• To select operating conditions to meet desired specifications, such as when
there are multiple specifications (one for each response) that must be met
simultaneously

Methodology

The general technique for RSA, sometimes referred to as the sequential RSA
technique, involves two phases (phase 1 and phase 2) and a prerequisite
(phase 0) (Myers and Montgomery, 1995).
Phase 0 is the use of screening designs to narrow the list of potential factors
down to a critical set of significant factors and develop a first-order regression
model. RSA should not be started until this work has been completed.
In phase 1, the steepest ascent methodology is used to define the current

operating region and determine the direction of maximum response. (When
seeking to minimize the response variable, the technique is sometimes referred
to as steepest descent). Phase 1 uses the first-order model generated earlier
because of its economy of data collection. The 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 we are not
interested in a detailed mapping of the response region far away from the
optimum.
Phase 2 will use a second-order model and ridge analysis techniques within
a small region to locate the optimal conditions, which occur at a stationary
point. A stationary point is the point where the slope of the second-order
response surface model with respect to each of the factors is zero. A stationary