MEASURING THE VOLUMES OF SODA CANS

The file Soda Cans.xlsx contains data on the number of ounces of soda in cans labeled “12-ounce” cans. Every half hour, five cans of soda from a production process were measured for fill volume. This was done for 70 consecutive half-hour periods. Create and interpret the $\bar{X}$ and R charts.

Objective To use $\bar{X}$ and R charts to check whether the process of filling soda cans is performing as it should.

Question

MEASURING THE VOLUMES OF SODA CANS

The file Soda Cans.xlsx contains data on the number of ounces of soda in cans labeled “12-ounce” cans. Every half hour, five cans of soda from a production process were measured for fill volume. This was done for 70 consecutive half-hour periods. Create and interpret the [latex]\bar{X}[/latex] and R charts.

Objective To use [latex]\bar{X}[/latex] and R charts to check whether the process of filling soda cans is performing as it should.

Accepted Answer

Although [latex]\bar{X}[/latex] and R charts are quite easy to create by hand—this is the way they are often created on the shop floor—the process is tedious and better suited for computer implementation. We have done so in StatTools and will explain the steps here. First, the Soda Cans.xlsx file is set up in the appropriate way for StatTools. There are five adjacent columns for the five observations taken each half hour. (These columns need not be adjacent, but that is the natural arrangement.)

To use StatTools, designate the data range as a StatTools data set in the usual way, and then select X/R Charts from the Quality Control group on the StatTools ribbon. Fill in the resulting dialog box as shown in Figure 20.3. In particular, select the variables Can Fill Volumes Obs1 through Obs5, limit the graph to observations 1 to 30, and base the control limits only on these observations.

StatTools creates a new sheet called X-R Charts. It contains the data that the control charts are based on, along with the [latex]\bar{X}[/latex] and R charts. These charts appear in Figures 20.4 and 20.5. On each chart, you can see that the points vary around a centerline and stay within upper and lower control limits (although one point on the [latex]\bar{X}[/latex] chart is very close to the upper limit). The behavior in these charts is typical in-control behavior. No points are outside of the control limits, and there is no obvious “nonrandom” behavior, such as an upward trend through time. Therefore, this process appears to be in control. If there are specifications on the soda cans—for example, the fill volume of a can should be between 11.88 and 12.20 ounces—then we could use the data (and the fact that the process is in control, that is, predictable) to estimate the percentage of all cans within specs. Again, this percentage might not be as high as the company would like, but at least it’s predictable.

Question 20.1.a: MEASURING THE VOLUMES OF SODA CANS The file Soda Cans.xlsx c......

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