Applied Statistics and Probability for Engineers

628 CHAPTER 16 STATISTICAL QUALITY CONTROL

These control limits are based on the normal approximation to the Poisson distribution.

When is small, the normal approximation may not always be adequate. In such cases, we

may use control limits obtained directly from a table of Poisson probabilities. If is small,

the lower control limit obtained from the normal approximation may be a negative number.

If this should occur, it is customary to consider zero as the lower control limit.

EXAMPLE 16-5 Printed circuit boards are assembled by a combination of manual assembly and automation. A

flow solder machine is used to make the mechanical and electrical connections of the leaded

components to the board. The boards are run through the flow solder process almost continu-

ously, and every hour five boards are selected and inspected for process-control purposes. The

number of defects in each sample of five boards is noted. Results for 20 samples are shown in

Table 16-5.

The center line for the Uchart is

and the upper and lower control limits are

The control chart is plotted in Fig. 16-17. Because LCLis negative, it is set to 0. From the con-

trol chart in Fig. 16-17, we see that the process is in control. However, eight defects per group

of five circuit boards are too many (about 8 5 1.6 defects/board), and the process needs

improvement. An investigation needs to be made of the specific types of defects found on the

printed circuit boards. This will usually suggest potential avenues for process improvement.

Computer software also produces aCchart.This is just a control chart of C, the total of

defects in a sample. The points, center line, and control limits for this chart are just multiples

LCLu 3

B

u

n1.6^3 B

1.6

5

0

UCLu 3

B

u

n1.6^3 B

1.6

5

3.3

u

1

20 a

20

i 1

ui

32

20

1.6

u

Table 16-5 Number of Defects in Samples of Five Printed Circuit Boards

Number of Defects per Number of Defects per

Sample Defects Unit ui Sample Defects Unit ui

1 6 1.2 11 9 1.8

2 4 0.8 12 15 3.0

3 8 1.6 13 8 1.6

4 10 2.0 14 10 2.0

5 9 1.8 15 8 1.6

6 12 2.4 16 2 0.4

7 16 3.2 17 7 1.4

8 2 0.4 18 1 0.2

9 3 0.6 19 7 1.4

10 10 2.0 20 13 2.6

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