Question#5 (5 marks) A manufacturing process makes turbine blades for turbocharg

Question

Question#5 (5 marks) 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?

Explanation / Answer

a)

here xbar =21 and Rbar =12.4

for mean chart: for sample size n=5 per day ; constant A2 =0.577

hence upper control limit of mean =Xbar +A2*Rbar=28.15

lower control limit of mean =Xbar -A2*Rbar=13.85

for range chart: for sample size n=5 per day ; constant D3=0 and D4=2.115

upper control limit of Range =D4*Rbar=2.115*12.4=26.23

lower control limit of Range =D3*R =0*12.4=0

b)

as mean value 30 false outside the upper control limit ; therefore we may conclude that process is out of control

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