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 $($A$2=1\mathrm{.}023,$ D$3=0,$ D$4=2\mathrm{.}574)$

Outside diameter $($millimeters$)$

Time Period $3$ samples pulled each time period X$-$Bar Range

$8$:$00342$

$8$:$30453$

$9$:$00222$

$9$:$30123$

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:

Rubric:

Quality Control Chart Skills Outcome

Unacceptable $(1$ pt$)$ Partially proficient $(2$ pts$)$ Proficient $(3$ pts$)$ Accomplished $(4$ pts$)$

A$.$ The student is unable to calculate the average and the range. The student can calculate the average and the range. However the student is not able to calculate the average range and the average of the averages. The student can calculate the average and the range. The student is able to calculate the average range and the average of the averages. The student cannot calculate the upper and lower control limits$.$ The student can calculate the average and the range. The student is able to calculate the average range and the average of the averages. The student can also calculate the upper and lower control limits$.$

B$.$ The student does not understand the problem well enough to plot a control chart. The student is able to plot the control chart identifying the process center, upper control limit and lower control limit$.$ However, the student makes major errors. The student is able to plot the control chart identifying the process center, upper control limit and lower control limit$.$ However, the student makes minor errors. The student is able to plot the control chart identifying the process center, upper control limit and lower control limit$.$

C$.$ The student is unable to comment on the control chart. The student is able to comment on the control chart. However, there are major errors in this discussion. The student is able to comment on the control chart. However, there are minor errors in this discussion. The student is able to comment on the control chart, identifying any points that are in control or out of control.