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

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for this problem.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

1010

pistons produced each day, the mean and the range of this diameter have been as follows:

Day	Mean Bold x overbarx (mm)	Range R (mm)
1	156.9156.9	4.44.4
2	151.2151.2	4.84.8
3	155.6155.6	3.93.9
4	155.5155.5	5.05.0
5	154.6154.6	4.54.5

a) What is the value of

x double overbarx?

x double overbarxequals=nothing

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

Upper R overbarR?

Upper R overbarRequals=nothing

mm (round your response to two decimal places).c) What are the

UCL Subscript x overbarUCLx

and

LCL Subscript x overbarLCLx

using

3-sigma?

Upper Control Limit

(UCL Subscript x overbarUCLx)

=

nothing

mm (round your response to two decimal places).Lower Control Limit

(LCL Subscript x overbarLCLx)

=

nothing

mm (round your response to two decimal places).d) What are the

UCL Subscript Upper RUCLR

and

LCL Subscript Upper RLCLR

using

3-sigma?

Upper Control Limit

(UCL Subscript Upper RUCLR)

=

nothing

mm (round your response to two decimal places).Lower Control Limit

(LCL Subscript Upper RLCLR)

=

nothing

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

UCL Subscript x overbarUCLx

and

LCL Subscript x overbarLCLx?

Upper Control Limit

(UCL Subscript x overbarUCLx)

=

nothing

mm (round your response to two decimal places).Lower Control Limit

(LCL Subscript x overbarLCLx)

=

nothing

mm (round your response to two decimal places).

Enter your answer in each of the answer boxes.

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