Question

Minting Quarters Specifications for a quarter require that it be 8.33% nickel and 91.67% copper; it must weigh 5.670 g and have a diameter of 24.26 mm and a thickness of 1.75 mm; and it must have 119 reeds on the edge. A quarter is considered to be defective if it deviates substantially from those specifications. A production process is monitored, defects are recorded and the accompanying control chart is obtained. Does this process appear to be within statistical control? If not, identify any out-of-control criteria that are satisfied. Is the manufacturing process deteriorating?

Short answer

No, the process does not appear to be within statistical control.

The following out-of-control criteria are noticeable, which imply that the process is out of control:

• There is a downward trend.
• There are at least 8 points above the centerline.

No, the manufacturing process is not deteriorating. Rather, the process appears to be improving as the proportion of defective quarters are declining.

Step-by-step solution

Given information

A p-chart is plotted to examine if the process is under control or not.

Here, the p-chart depicts the proportion of defective quarters manufactured a series of times.

Analysis of the p-chart

The p-chart depicts the following two out-of-control criteria:

• There is a downward trend in the proportion of defective quarters as the points move from the upper left corner to the lower right corner.
• More than 8 points lieabove the central line.

Since the above two features imply that the process is not stable, it can be said that the process is not under statistical control.

Moreover, the proportion of defective quarters produced have decreased over time.

This indicates that the manufacturing process is bettering and not deteriorating.