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Chapter 19: B. Statistical Process Control 267
Continued
Sample mean
X – chart
1
UCL = 15.18814
15.18
15.16
15.14
X – = 15.1628
LCL = 15.13746
2 4 6 8 10 12 14 16 18 20 22 24
Sample
R chart
0.08 UCL = 0.07936
Sample range
0.06
0.04
0.02
0.00
2 4 6 8 10 12 14 16 18 20 22 24
Sample
R – = 0.03479
LCL = 0
Figure 19.8 X – and R control chart for the ball bearing data in Table 19.3.
It is customary to prepare the R chart first and verify that all the plotted points fall within
the control limits, and only then proceed to constructing the X – chart. In fact, the concept
of bringing the process variability under control first and then proceeding to control
the average does make a lot of sense. This is due to the fact that without controlling the
process variability, it is almost impossible to bring the process average under control.
The R chart for the data in Table 19.3 is given in Figure 19.8, which shows that all
the plotted points fall within the control limits and there is no evidence of any special
pattern. Thus, we may conclude that the only variation present in the process is due to
common causes. In this case we can proceed further to calculate the control limits for
the X – chart. From Appendix E for sample of size n = 4, we get A 2 = 0.729. Thus, we have
Part IV.B.3
LCL = x A 2
R = 15. 1628 0. 729× 0. 03479 = 15.
13746
UCL = x + A 2
R = 15. 1628+ 0. 729× 0. 03479 = 15. 18814.
The X – chart for the data is given in Figure 19.8, which shows that point 22 exceeds the
upper control limits. Moreover, there are too many consecutive points that fall below
the center line. This indicates that the process is not under control and there are some
special causes present that are affecting the process average. Thus, a thorough investigation
should be launched to find the special causes, and appropriate action should
be taken to eliminate these special causes before we proceed to recalculate the control
limits for the ongoing process.