Quality Control Chart

Student learning outcomes

Construct and demonstrate the application of control charts for monitoring process variation.

Problem:

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 the results. The measurements $($in millimeters$)$ for the period $8$:$00$ AM to $9$:$30$ AM follow. Note quality control constant $(A2=1\mathrm{.}023,D3=0,D4=2\mathrm{.}574)$

Outside diameter $($millimeters$)$

$\backslash$table$[[$Time Period,$3$ samples pulled each time period,X$-$Bar,Range,,$],[8$:$00,3,4,2,,],[8$:$30,4,5,3,,],[9$:$00,2,2,2,,],[9$:$30,1,2,3,,],[,,,,,]]$

a$.$ Determine the control limits for the mean and the range.

b$.$ Plot the control limits far the mean outside diameter and the range.

c$.$ Are there any points on the mean or the range chart that are out of control? Comment on the chart: