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) 1 156.9 4.4 2 155.2 4.4 3 155.6 4.3 4 153.5 4.8 5 156.6 4.7 Part 2 a) What is the value of x? x= _______ mm (round your response to two decimal places). b) What is the value of Upper R overbarR ? Upper R overbarRequals= _______ 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 ) = _________ mm (round your response to two decimal places). Lower Control Limit (LCL Subscript x overbarLCLx ) = ________ 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 ) = __________ mm (round your response to two decimal places). Lower Control Limit (LCL Subscript Upper RLCLR ) = __________ 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 ) = _________ mm (round your response to two decimal places). Lower Control Limit (LCL Subscript x overbarLCLx ) = ________ mm (round your response to two decimal places).
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) 1 156.9 4.4 2 155.2 4.4 3 155.6 4.3 4 153.5 4.8 5 156.6 4.7 Part 2 a) What is the value of x? x= _______ mm (round your response to two decimal places). b) What is the value of Upper R overbarR ? Upper R overbarRequals= _______ 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 ) = _________ mm (round your response to two decimal places). Lower Control Limit (LCL Subscript x overbarLCLx ) = ________ 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 ) = __________ mm (round your response to two decimal places). Lower Control Limit (LCL Subscript Upper RLCLR ) = __________ 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 ) = _________ mm (round your response to two decimal places). Lower Control Limit (LCL Subscript x overbarLCLx ) = ________ mm (round your response to two decimal places).
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter10: Introduction To Simulation Modeling
Section10.2: Probability Distributions For Input Variables
Problem 2P: Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with...
Related questions
Question
4.
Refer to
Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)
for this problem.LOADING...
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
|
156.9
|
4.4
|
|
2
|
155.2
|
4.4
|
|
3
|
155.6
|
4.3
|
|
4
|
153.5
|
4.8
|
|
5
|
156.6
|
4.7
|
Part 2
a) What is the value of
x?
x= _______ mm (round your response to two decimal places).
b) What is the value of
Upper R overbarR ?
Upper R overbarRequals= _______ 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 )
= _________ mm (round your response to two decimal places).
Lower Control Limit
(LCL Subscript x overbarLCLx )
= ________ 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 )
= __________ mm (round your response to two decimal places).
Lower Control Limit
(LCL Subscript Upper RLCLR )
= __________ 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 )
= _________ mm (round your response to two decimal places).
Lower Control Limit
(LCL Subscript x overbarLCLx )
= ________ mm (round your response to two decimal places).
Transcribed Image Text:Sample
Size, n
234
2
5
6
7
8
9
10
12
Mean Factor,
A2
1.880
1.023
0.729
0.577
0.483
0.419
0.373
0.337
0.308
0.266
Upper Range,
D4
3.268
2.574
2.282
2.115
2.004
1.924
1.864
1.816
1.777
1.716
Lower Range,
D3
0
0
0
0
0.076
0.136
0.184
0.223
0.284
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