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

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 x (mm)	Range R (mm)
1	154.9	4.2
2	155.2	4.4
3	155.6	3.9
4	157.5	5.2
5	154.6	4.7

Part 2

a) What is the value of

x?

x=enter your response here

mm (round your response to two decimal places).

Part 3

b) What is the value of

R?

R=enter your response here

mm (round your response to two decimal places).

Part 4

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).

Part 5

Lower Control Limit

(LCLx)

=

enter your response here

mm (round your response to two decimal places).

Part 6

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).

Part 7

Lower Control Limit

(LCLR)

=

enter your response here

mm (round your response to two decimal places).

Part 8

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)

=

enter your response here

mm (round your response to two decimal places).

Part 9

Lower Control Limit

(LCLx)

=

enter your response here

mm (round your response to two decimal places).