Applied Statistics and Probability for Engineers

increases most rapidly. This direction is normal to the fitted response surface contours. We

usually take as the path of steepest ascentthe line through the center of the region of interest

and normal to the fitted surface contours. Thus, the steps along the path are proportional to the

regression coefficients. The experimenter determines the actual step size based on

process knowledge or other practical considerations.

Experiments are conducted along the path of steepest ascent until no further increase in

response is observed. Then a new first-order model may be fit, a new direction of steepest as-

cent determined, and further experiments conducted in that direction until the experimenter

feels that the process is near the optimum.

5 ˆi 6

yˆ

14-14

30.00

150.0

31.67 33.33 35.00 36.67 38.33 40.00

39.50

40.00

40.50

41.00

41.50

151.7

153.3

155.0

156.7

158.3

1 160.0

• 1

x^2

(temperature)

x 1 (time)

• 1+1 0

0

Contour plot

(a)

40.00

38.00

(b)

36.00

34.00

32.00

150.030.00

152.0

154.0

156.0

158.0

160.0

39.00

41.00

43.00

45.00

x 2 (temperature) x 1 (time)

Conversion

+1

(^00)
+1

• 1 – 1
  Three-dimensional surface plot

Figure S14-8 Response surface plots for the first-order model

in Example S14-3.

PQ220 6234F.CD(14) 5/9/02 8:39 PM Page 14 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L: