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272 Part IV: Quality Assurance
EXAMPLE 19.5
Use the ball bearing data in Table 19.3 to construct X – and S control charts.
Solution:
From Appendix E for sample of size n = 4, we have B 3 = 0, and B 4 = 2.266. Thus, the control
limits for the S control chart are
LCL = Bs
3
= 0× 0.
01557 = 0
UCL = Bs= 2. 266× 0. 01557 = 0.03527.
4
It is customary to prepare the S control chart first and verify that all the plotted points
fall within the control limits and only then proceeding to construct the X – control chart.
As described earlier, the concept of first bringing the process variability under control
and only then proceeding to control the average does make lot of sense, since without
controlling the process variability, it is practically impossible to bring the process average
under control.
The S chart for the data is given in Figure 19.9, which shows that points two and
three almost coincide with the upper control limit. Moreover, point 17 is almost on the
center line. If this point were clearly below the center line then we would have had a
run of nine points below the center line. These observations indicate that the process
variability is marginally under control and, therefore, the process should be carefully
monitored. Since the process variability is under control, even though marginally, 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 3 = 1.628. Thus, we have
LCL = x A 3
s = 15. 1628 1. 628× 0. 01557 = 15.
13746
UCL = x + A 3
s = 15. 1628+ 1. 628× 0. 01557 = 15. 1881.
Part IV.B.3
The X – chart for the data in Table 19.3 is given in Figure 19.9, 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 in 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 proceeding to recalculate
the control limits for an ongoing process.
Continued