STATISTICAL QUALITY CONTROL in .NET

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CHAPTER 16 STATISTICAL QUALITY CONTROL
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EXERCISES FOR SECTION 16-5
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16-1. An extrusion die is used to produce aluminum rods. The diameter of the rods is a critical quality characteristic. The following table shows x and r values for 20 samples of ve rods each. Speci cations on the rods are 0.5035 0.0010 inch. The values given are the last three digits of the measurement; that is, 34.2 is read as 0.50342. Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x 34.2 31.6 31.8 33.4 35.0 32.1 32.6 33.8 34.8 38.6 35.4 34.0 36.0 37.2 35.2 33.4 35.0 34.4 33.9 34.0 r 3 4 4 5 4 2 7 9 10 4 8 6 4 7 3 10 4 7 8 4 (b) Use the control limits from part (a) to identify out-of-control points. If necessary, revise your control limits assuming that any samples that plot outside of the control limits can be eliminated. (c) Repeat parts (a) and (b) for X and S charts. Sample Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x1 15.4 15.4 16.1 13.5 18.3 19.2 14.1 15.6 13.9 18.7 15.3 16.6 17.0 16.3 8.4 11.1 16.5 18.0 17.8 11.5 x2 15.6 17.1 16.1 12.5 16.1 17.2 12.4 13.3 14.9 21.2 13.1 18.0 15.2 16.5 7.7 13.8 17.1 14.1 17.3 10.8 x3 15.3 15.2 13.5 10.2 17.0 19.4 11.7 13.6 15.5 20.1 13.7 18.0 18.1 17.7 8.4 11.9 18.5 15.9 12.0 11.2
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(a) Using all the data, nd trial control limits for X and R charts, construct the chart, and plot the data. (b) Use the trial control limits from part (a) to identify out-of-control points. If necessary, revise your control limits, assuming that any samples that plot outside the control limits can be eliminated. 16-2. Twenty-five samples of size 5 are drawn from a process at one-hour intervals, and the following data are obtained:
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16-4. Samples of size n 6 are collected from a process every hour. After 20 samples have been collected, we calculate x 20.0 and r d2 1.4. (a) Find trial control limits for X and R charts. (b) If s c4 1.5 , determine trial control limits for X and S charts. 16-5. Control charts for X and R are to be set up for an important quality characteristic. The sample size is n 5, and x and r are computed for each of 35 preliminary samples. The summary data are
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(a) Find trial control limits for X and R charts. (b) Repeat part (a) for X and S charts. 16-3. The pull strength of a wire-bonded lead for an integrated circuit monitored. The following table provides data for 20 samples each of size three. (a) Use all the data to determine trial control limits for X and R charts, construct the control limits, and plot the data.
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(a) Find trial control limits for X and R charts. (b) Assuming that the process is in control, estimate the process mean and standard deviation. 16-6. Control charts are to be constructed for samples of size n 4, and x and s are computed for each of 20 preliminary samples as follows:
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16-6 CONTROL CHARTS FOR INDIVIDUAL MEASUREMENTS
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(a) Determine trial control limits for X and S charts. (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 quality parameter. Data on thickness (in inches) are given in the following table, for 25 samples of ve parts each. Sample Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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x1 0.0629 0.0630 0.0628 0.0634 0.0619 0.0613 0.0630 0.0628 0.0623 0.0631 0.0635 0.0623 0.0635 0.0645 0.0619 0.0631 0.0616 0.0630 0.0636 0.0640 0.0628 0.0615 0.0630 0.0635 0.0623
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x2 0.0636 0.0631 0.0631 0.0630 0.0628 0.0629 0.0639 0.0627 0.0626 0.0631 0.0630 0.0630 0.0631 0.0640 0.0644 0.0627 0.0623 0.0630 0.0631 0.0635 0.0625 0.0625 0.0632 0.0629 0.0629
x3 0.0640 0.0622 0.0633 0.0631 0.0630 0.0634 0.0625 0.0622 0.0633 0.0633 0.0638 0.0630 0.0630 0.0631 0.0632 0.0630 0.0631 0.0626 0.0629 0.0629 0.0616 0.0619 0.0630 0.0635 0.0630
x4 0.0635 0.0625 0.0633 0.0632 0.0619 0.0625 0.0629 0.0625 0.0630 0.0631 0.0635 0.0627 0.0630 0.0640 0.0622 0.0628 0.0620 0.0629 0.0635 0.0635 0.0620 0.0619 0.0631 0.0631 0.0626
x5 0.0640 0.0627 0.0630 0.0633 0.0625 0.0628 0.0627 0.0627 0.0624 0.0630 0.0633 0.0629 0.0630 0.0642 0.0635 0.0629 0.0625 0.0628 0.0634 0.0634 0.0623 0.0622 0.0630 0.0633 0.0628
(a) Using all the data, nd trial control limits for X and R charts, construct the chart, and plot the data. Is the process in statistical control (b) Repeat part (a) for X and S charts. (c) Use the trial control limits from part (a) to identify out-ofcontrol 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 x and r values for 25 days are shown in the following table: (a) Using all the data, nd trial control limits for X and R charts, 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 1 2 3 4 5 6 7 8 9 10 11 12 13 x 5.45 5.39 6.85 6.74 5.83 7.22 6.39 6.50 7.15 5.92 6.45 5.38 6.03 r 1.21 0.95 1.43 1.29 1.35 0.88 0.92 1.13 1.25 1.05 0.98 1.36 0.83 Day 14 15 16 17 18 19 20 21 22 23 24 25 x 7.01 5.83 6.35 6.05 7.11 7.32 5.90 5.50 6.32 6.55 5.90 5.95 r 1.45 1.37 1.04 0.83 1.35 1.09 1.22 0.98 1.21 0.76 1.20 1.19
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