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# How do you determine the control limits for the mean and range for the outside diameter of slugs made by a new machine?

A new machine has just been installed to cut and rough-shape large slugs. The slugs are then transferred to a precision grinder. One of the critical measurements is the outside diameter. The quality control inspector randomly selected five slugs each hour, measured the outside diameter, and recorded dthe results. The measurements (in millimeters) for the period 8:00 a.m. to 10:30 a.m follow.

Outside Diameter (millimeters)

Time 1 2 3 4 5
8:00 87.1 87.3 87.9 87.0 87.0
8.:30 86.9 88.5 87.6 87.5 87.4
9:00 87.5 88.4 86.9 87.6 88.2
9:30 86.0 88.0 87.2 87.6 87.1
10:00 87.1 87.1 87.1 87.1 87.1
10:30 88.0 86.2 87.4 87.3 87.8

a. Determine the control limits for the mean and the range.
b. Plot the control limits for the mean outside diameter and the range.

#### Solution Preview

Student,

question a:
The control limits for the mean are 86.62 ...

#### Solution Summary

This solution shows how to determine the lower control limit and the upper control limit for the average and the range in an attached Excel file. The x-bar and range control chart are also compiled.

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