Page 383 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 363

more centerpoints (to estimate curvature) and one or more replicated runs to
estimate lack of fit.
If the lack of fit is not significant, then determine a new path of steepest
ascent by varying the starting point, intervals, or direction along the first-order
model. If lack of fit is significant and curvature is present, then this suggests
that you are near a stationary point, which may be a local maximum, mini-
mum, or saddle point (a maximum in one factor, minimum in another). At this
point, stop the steepest ascent methodology and proceed to phase 2 ridge
analysis.

Phase 2: Ridge Analysis

The graphic method for ridge analysis is as follows:
1. Use a central composite design near the optimum (defined in the RSA) to
generate a second-order regression model.
2. Generate contour plots and response surface plots for each pair of factors.

3. Determine the stationary point (the local minimum, maximum, or saddle
point as described earlier) from the plots.

4. Calculate the predicted response at the optimum using the second-order
regression model.

5. Collect new data in the region of the optimum to verify the model.
In practice, many processes must achieve optimality with respect to more
than one response. For example,

• Cost and yield in chemical, manufacturing, and health-care processes

• Cost and customer satisfaction in service processes
• Efficacy of drug and minimal side effects in pharmaceutical processes
• Timeliness of service and cost in service processes

For multiple responses, overlaid contour plots (see “Contour Plot”) or desir-
ability functions can be used.
Derringer and Suich (1980) developed an analytical approach to determin-
ing the simultaneous optima for several responses, known as a desirability func-
tion (Myers and Montgomery, 1995). Minitab provides a calculation of the
desirability function given the input parameters discussed below. For each
response, we define the goal as either a minimization, a maximization, or a
specified target value. Each response is weighted with respect to meeting its