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

a. For daily means :

Lower control limit = mean - A₂* mean of range

For n= 10 , A₂ = 0.31

LCL = 21 - 0.31*12.4 = 17.156

UCL = 21 + 0.31*12.4 = 24.844

For ranges :

LCL = D₃ * Mean of range  

UCL = D₄ * mean of range

For n = 10 , D₃ = 0.22 and D₄ = 1.78

LCL = 0.22 * 12.4 = 2.728

UCL = 1.78 * 12.4 = 22.072

b. Here we can see that mean = 30 is greater than UCL for daily mean , hence , we can say that the process is not in control or out of control.

Range = 17.8 lies between the UCL and LCL for range.