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 wene 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)

Given, Mean of Means (X) = 21gm

And Mean of Ranges (R) = 12.4gm

For n = 5, A = 0.58 (since 5 subgroups were taken on each of the 10 days)

Means

Upper Control Limit (UCL) = X + A* R = 21 + 0.58 * 12.4 = 28.19

Similarly,

Lower Control Limit (LCL) = X - A* R = 21 - 0.58 * 12.4 = 13.81

Ranges

D4 = 2.114 and D3 = 0 for n = 5

Upper Control Limit (UCL) = D4* R = 2.114 * 12.4 = 26.21

Similarly,

Lower Control Limit (LCL) = D3* R = 0* 12.4 = 0

b)

On one day, Mean = 30 and Range = 17.8gm

Since the Mean is above the UCL, the process is out of control and an investigation is needed to find and eliminate the cause or causes.

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