16-6 CONTROL CHARTS FOR INDIVIDUAL MEASUREMENTS 615(a) Determine trial control limits for and Scharts.
(b) Assuming the process is in control, estimate the process
mean and standard deviation.
16-7. The thickness of a metal part is an important qual-
ity parameter. Data on thickness (in inches) are given in the
following table, for 25 samples of five parts each.X (a) Using all the data, find trial control limits for and R
charts, construct the chart, and plot the data. Is the process
in statistical control?
(b) Repeat part (a) for and Scharts.
(c) Use the trial control limits from part (a) to identify out-of-
control points. List the sample numbers of the out-of-control
points.
16-8. The copper content of a plating bath is measured three
times per day, and the results are reported in ppm. The and r
values for 25 days are shown in the following table:
(a) Using all the data, find trial control limits for and Rcharts,
construct the chart, and plot the data. Is the process in
statistical control?
(b) If necessary, revise the control limits computed in part (a),
assuming that any samples that plot outside the control
limits can be eliminated.Day r Day r
1 5.45 1.21 14 7.01 1.45
2 5.39 0.95 15 5.83 1.37
3 6.85 1.43 16 6.35 1.04
4 6.74 1.29 17 6.05 0.83
5 5.83 1.35 18 7.11 1.35
6 7.22 0.88 19 7.32 1.09
7 6.39 0.92 20 5.90 1.22
8 6.50 1.13 21 5.50 0.98
9 7.15 1.25 22 6.32 1.21
10 5.92 1.05 23 6.55 0.76
11 6.45 0.98 24 5.90 1.20
12 5.38 1.36 25 5.95 1.19
13 6.03 0.83x xXxXX16-6 CONTROL CHARTS FOR INDIVIDUAL
MEASUREMENTSIn many situations, the sample size used for process control is n1; that is, the sample con-
sists of an individual unit. Some examples of these situations are as follows:- Automated inspection and measurement technology is used, and every unit manu-
factured is analyzed. - The production rate is very slow, and it is inconvenient to allow sample sizes of n 1
to accumulate before being analyzed. - Repeat measurements on the process differ only because of laboratory or analysis
error, as in many chemical processes.
Sample
Number x 1 x 2 x 3 x 4 x 5
1 0.0629 0.0636 0.0640 0.0635 0.0640
2 0.0630 0.0631 0.0622 0.0625 0.0627
3 0.0628 0.0631 0.0633 0.0633 0.0630
4 0.0634 0.0630 0.0631 0.0632 0.0633
5 0.0619 0.0628 0.0630 0.0619 0.0625
6 0.0613 0.0629 0.0634 0.0625 0.0628
7 0.0630 0.0639 0.0625 0.0629 0.0627
8 0.0628 0.0627 0.0622 0.0625 0.0627
9 0.0623 0.0626 0.0633 0.0630 0.0624
10 0.0631 0.0631 0.0633 0.0631 0.0630
11 0.0635 0.0630 0.0638 0.0635 0.0633
12 0.0623 0.0630 0.0630 0.0627 0.0629
13 0.0635 0.0631 0.0630 0.0630 0.0630
14 0.0645 0.0640 0.0631 0.0640 0.0642
15 0.0619 0.0644 0.0632 0.0622 0.0635
16 0.0631 0.0627 0.0630 0.0628 0.0629
17 0.0616 0.0623 0.0631 0.0620 0.0625
18 0.0630 0.0630 0.0626 0.0629 0.0628
19 0.0636 0.0631 0.0629 0.0635 0.0634
20 0.0640 0.0635 0.0629 0.0635 0.0634
21 0.0628 0.0625 0.0616 0.0620 0.0623
22 0.0615 0.0625 0.0619 0.0619 0.0622
23 0.0630 0.0632 0.0630 0.0631 0.0630
24 0.0635 0.0629 0.0635 0.0631 0.0633
25 0.0623 0.0629 0.0630 0.0626 0.0628c 16 .qxd 5/8/02 9:58 PM Page 615 RK UL 6 RK UL 6:Desktop Folder: