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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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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4. 

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
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).

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
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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