A pharmaceutical company fills a drug which is in a powder form into a bottle. It has an automated process consisting of a filling machine and a sealing unit. After filling the bottle, it is automatically sealed with a metallic cap. To monitor the quality of the process, samples of size 5 are drawn periodically from the process and the quantity filled is measured. The table below has data on 12 such observations. Sample 1 2 3 4 5 1 9.21 8.87 8.71 9.08 9.34 2 9.06 8.97 9.13 8.46 8.85 3 9.35 8.95 9.20 9.03 8.44 4 9.21 8.71 9.05 9.35 8.87 5 9.01 9.17 9.21 9.05 9.53 6 8.74 8.35 8.50 9.06 8.89 7 9.21 9.05 9.00 8.78 9.23 8 9.15 9.20 9.23 9.15 9.06 9 8.98 8.81 8.90 9.13 9.05 10 9.03 9.10 9.26 9.44 8.48 11 9.49 9.05 9.12 8.88 8.93 12 8.95 9.10 9.02 9.04 8.96 (a) Establish the upper and lower control limits for the X bar chart and the R Chart (b) Construct a control chart and investigate if the process is in control Values for setting the control charts are A2 = 0.577, D3 = 0, D4 = 2.114
A pharmaceutical company fills a drug which is in a powder form into a bottle. It has an automated
process consisting of a filling machine and a sealing unit. After filling the bottle, it is automatically
sealed with a metallic cap. To monitor the quality of the process, samples of size 5 are drawn
periodically from the process and the quantity filled is measured. The table below has data on 12
such observations.
Sample 1 2 3 4 5
1 9.21 8.87 8.71 9.08 9.34
2 9.06 8.97 9.13 8.46 8.85
3 9.35 8.95 9.20 9.03 8.44
4 9.21 8.71 9.05 9.35 8.87
5 9.01 9.17 9.21 9.05 9.53
6 8.74 8.35 8.50 9.06 8.89
7 9.21 9.05 9.00 8.78 9.23
8 9.15 9.20 9.23 9.15 9.06
9 8.98 8.81 8.90 9.13 9.05
10 9.03 9.10 9.26 9.44 8.48
11 9.49 9.05 9.12 8.88 8.93
12 8.95 9.10 9.02 9.04 8.96
(a) Establish the upper and lower control limits for the X bar chart and the R Chart
(b) Construct a control chart and investigate if the process is in control
Values for setting the control charts are A2 = 0.577, D3 = 0, D4 = 2.114
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