1st column SampleSize, n

2nd column Mean Factor, A2

3rd column Upper Range, D4

4th column Lower Range,D3

2	1.880	3.268	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.115	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223
12	0.266	1.716	0.284

Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

Day	Mean x (mm)	Range R (mm)
1	158.9	4.2
2	151.2	4.8
3	151.6	4.1
4	153.5	4.8
5	156.6	4.7

a) What is the value of x? x=.________mm (round your response to two decimal places).

b) What is the value of R?_________mm (round your response to two decimal places).

c) What are the UCLx and LCLx using 3-sigma?

Upper Control Limit (UCLx) =____mm (round your response to two decimal places).

Lower Control Limit (LCLx) =______mm (round your response to two decimal places).

d) What are the UCLR and LCLR using 3-sigma?

Upper Control Limit (UCLR) =________mm (round your response to two decimal places).

Lower Control Limit (LCLR) =__________mm (round your response to two decimal places).

e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCLx and LCLx?

Upper Control Limit (UCLx) =______mm (round your response to two decimal places).

Lower Control Limit (LCLx)=______mm (round your response to two decimal places).