Question 20.1.b: MEASURING THE VOLUMES OF SODA CANS (CONTINUED) We now assume......
MEASURING THE VOLUMES OF SODA CANS (CONTINUED)
We now assume that the first 30 subsamples of soda can fill volumes, the ones used previously in Example 20.1, were used to determine centerlines and control limits for the \bar{X} and R charts. When we plot the other 40 subsamples, using the same centerlines and control limits, what do we learn about the process?
Objective To continue the \bar{X} and R charts to learn whether the soda can process stays in control beyond the subsamples on which the original charts were based.
As the dialog box in Figure 20.3 indicates, StatTools allows you to choose the subsamples to plot, as well as the subsamples to base the control limits on. Here we will plot all of the subsamples but base the control limits (and centerlines) only on subsamples 1–30. The dialog box should be filled out as shown in Figure 20.6. The resulting \bar{X} and R charts appear in Figures 20.7 and 20.8.
We first look at the R chart. It shows that the process stayed in control for at least 10 more half-hour periods beyond subsample 30. However, beginning shortly after subsample 40, the process variability appears to have increased (many points above the centerline), and finally two points, subsamples 49 and 53, jumped above the upper control limit. As if this weren’t enough evidence of an upward shift in variability, because we checked the options for runs in the dialog box, we can also see runs of at least eight points above or below the centerline. (It is very unlikely to see a run this long in an in-control process.) StatTools colors such runs green.
Presumably, the operator of the process discovered the problem that was causing abnormally high variation and fixed it at around the time of subsample 55. After that point, the R chart goes back into control (where “in control” is relative to the first 30 subsamples). However, at about this same time, the X chart suggests a downward shift in the process mean. Many points are below the centerline, and one finally crosses the lower control limit on subsample 63. Many machines have a mechanism for adjusting the mean to some target level, such as 12.05 ounces. In the present case, it appears that this machine simply needs to be readjusted to bring its mean back up to the previous level. After this is done, both of the control charts should indicate an in-control process—at least until some other assignable cause forces it out of control again.
This example illustrates how control charts allow an operator to monitor a process continuously and react quickly when problems are indicated. Without this continuous monitoring, out-of-control conditions could persist indefinitely, causing poor quality and higher costs.
