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. Mean = 21 Range = 12.4 (both in gm.)

We know, we can estimate SD from range, as
SD = Range/4

Therefore, SD = 12.4/4 = 3.1 (in gm.)

Now, UCL = mean + 3*SD
& LCL = mean - 3*SD

For means,
UCL = 21 + 3*3.1
= 30.3 gm.

LCL = 21- 3*3.1
= 11.7 gm.

For ranges,
UCL = 12.4 + 3*3.1
= 21.7 gm.

LCL = 12.4 - 3*3.1
= 3.1 gm.

b. The process can be said as in-control process, as both the observations lie below the UCL and above the LCL of respective categories.
As 30 lie between 11.7 and 30.3
& 17.8 lies between 3.1 and 21.7 .

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