Applied Statistics and Probability for Engineers

number of defects, and assist in determining which process variables should be carefully con-

trolled during manufacturing to prevent high defect levels and erratic process performance.

An Optimization Experiment

In a characterization experiment, we are interested in determining which factors affect the

response. A logical next step is to determine the region in the important factors that leads

to an optimum response.For example, if the response is cost, we will look for a region of

minimum cost.

As an illustration, suppose that the yield of a chemical process is influenced by the op-

erating temperature and the reaction time. We are currently operating the process at 155F

and 1.7 hours of reaction time, and the current process yield is around 75%. Figure S14-2

shows a view of the time–temperature space from above. In this graph we have connected

points of constant yield with lines. These lines are yield contours,and we have shown the

contours at 60, 70, 80, 90, and 95% yield. To locate the optimum, we might begin with a

factorial experiment such as we described below, with the two factors, time and temperature,

14-2

Input Output

...

Controllable factors

x 1 x 2 xp

z 1 z 2 zq

Uncontrollable (noise) factors

...

(printed circuit boards) (defects, y)

Process

(flow solder machine)

Figure S14-1 The

flow solder

experiment.

Figure S14-2

Contour plot of yield

as a function of reac-

tion time and reaction

temperature, illustrat-

ing an optimization

experiment.

0.5

140

1.0 1.5

Time (hr)

2.0 2.5

150

160

170

180

190

200

Temperature (

°F)

95%

Current

operating

conditions

90%

82%

70%

60%

58%

80%

75%

56% 69%

Path leading to region

of higher yield

PQ220 6234F.CD(14) 5/9/02 8:39 PM Page 2 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L: