Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem.

Sample Size, n	Mean Factor, A2	Upper Range, D4	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 Xbar (mm) Range R (mm) 1 156.9 4.2 2 153.2 4.4 3 151.6 3.9 4 157.5 5.2 5 156.6 4.3

a) What is the value of x?

x=enter your response here mm (round your response to two decimal places).

b) What is the value of R?

R=enter your response here mm (round your response to two decimal places).

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

Upper Control Limit (UCLx) = enter your response here mm (round your response to two decimal places).

Lower Control Limit (LCLx) = enter your response here mm (round your response to two decimal places).

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

Upper Control Limit (UCLR) = enter your response here mm (round your response to two decimal places).

Lower Control Limit (LCLR) = enter your response here mm (round your response to two decimal places).