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It is proposed to monitor and control the output of a shaft-production machine by drawing samples of six shafts

from the output of the machine every 30 minutes and measuring the diameters of the six shafts. To set up the control chart, data from 20 samples are analyzed to yield the following results: (i) the average of (the average of) the 20 samples = 5.0000 inches, and (ii) the average of the ranges of the 20 samples = 0.2000 inches. The UCL and LCL for the control chart for x-bar are

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control chart.jpg

Table of Control Chart Constants
X-bar Chart
Constants
for sigma
R. Chart Constants
estimate
S Chart Constants
Sample
Size = m
A;
D3
DA
B3
BA
1.880
2.659
1.128
0
3.267
0
1.023
1.954
1.693
3.267...

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