A process with a target of 25 was used to generate the following data points. Is the process properly centered? Determine the process capability given a USL = 27 and LSL = 18. The standard deviation of the data is 2.712
Sample 1 29.5 23 20.9 24.9
Sample 2 22.9 20.1 23.7 26.9
Sample 3 25.9 23.6 23 24.3
Sample 4 25.3 23.2 29.8 22.3
Sample 5 24.7 25.1 20.6 23
Sample 6 28.4 29.7 27.1 23.7
Sample 7 21.9 23.5 24.9 24.2
Sample 8 26.9 21.1 28.1 20.2
Sample 9 25.5 27.6 26.3 27.2
Sample 10 23.9 28.6 21.7 20.6
The sample means and ranges are contained in this table
X bar Range
24.6 8.6
23.4 6.8
24.2 2.9
25.2 7.5
23.4 4.5
27.2 6
23.6 3
24.1 7.9
26.7 2.1
23.7 8
The overall average is 24.6, and the average range is 5.73., so the process is not centered.
Using a value of 0.729 for the A2 lookup from Table 5.1 yields:
UCL = 24.6 + 0.729*5.73 = 28.8
LCL = 24.6 - .729*5.73 = 20.4
The chart is in control, so a process capability index has meaning. The standard deviation is 2.712.
Cpk = Minimum of
= Min = Min[0.81, 0.29] = 0.29
Wow, that's sad!
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