Question

A manufacturing process makes turbine blades for turbochargers used in racing cars. For ten days, a total of 50 observations were made on a manufacturing process. Every day, the mean and range were calculated for that day and at the end of ten days, it was found that the mean of all the ten mean was 21.0 gm and the mean of all the ten ranges was 12.4 gm. a. Calculate the Upper Control Limit (UCL) and the Lower Control Limit for both the daily means and ranges. b. If on one of the days, it was found that mean was 30.0 gm and range was 17.8 gm, what can say about the process?

Answer 1

it is given that  

number of subgroups k=10

For Daily means:

Upper Control Limit (UCL) =

Lower Control Limit (LCL) =

For Daily Ranges:

Upper Control Limit (UCL) =

Lower Control Limit (LCL) =

b) Always look at the Range chart first. The control limits on the X-bar chart are derived from the average range, so if the Range chart is out of control, then the control limits on the X-bar chart are meaningless.

range 17.8 is within control limits.

Mean 30 gm is not within control limits. Hence we can say that process is out of control