Samples of size four were taken from a process that had a target of 25 ounces with upper and lower specification limits of 30 ounces and 20 ounces respectively. Create the appropriate control charts and determine whether the process is in control
Then compute process capability.
Sample 1 29.5 23.0 22.0 24.9
Sample 2 22.9 22 23.7 26.9
Sample 3 25.9 23.6 23.0 24.3
Sample 4 25.3 23.2 29.8 22.3
Sample 5 24.7 25.1 24.5 23.0
Sample 6 28.4 29.7 27.1 23.7
Sample 7 21.9 23.5 24.9 24.2
Sample 8 26.9 26.2 28.1 20.2
Sample 9 25.5 27.6 26.3 27.2
Sample 10 23.9 28.6 21.7 20.6
This is variables data, so x-bar and R charts are the appropriate control charts for this process. The overall process average is 25, with a standard deviation of 2.406
The chart calculations are summarized in this table:
X bar CenterX UCLx LCLx Range Rbar UCLr LCLr
Sample 1 24.85 25.00 28.70 21.30 7.50 5.08 11.59 0.00
Sample 2 23.88 25.00 28.70 21.30 4.90 5.08 11.59 0.00
Sample 3 24.20 25.00 28.70 21.30 2.90 5.08 11.59 0.00
Sample 4 25.15 25.00 28.70 21.30 7.50 5.08 11.59 0.00
Sample 5 24.33 25.00 28.70 21.30 2.10 5.08 11.59 0.00
Sample 6 27.23 25.00 28.70 21.30 6.00 5.08 11.59 0.00
Sample 7 23.63 25.00 28.70 21.30 3.00 5.08 11.59 0.00
Sample 8 25.35 25.00 28.70 21.30 7.90 5.08 11.59 0.00
Sample 9 26.65 25.00 28.70 21.30 2.10 5.08 11.59 0.00
Both charts reflect a process that is in control.
The process capability ratio is 0.69
(USL-LSL)/(6*σ) = (30-20)/(6*2.406)=10/14.436=0.69
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