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 Bold x overbarx (mm) Range R (mm) 1 154.9154.9 4.04.0 2 151.2151.2 4.44.4 3 153.6153.6 3.93.9 4 155.5155.5 5.05.0 5 158.6158.6 4.3 a) What is the value of x? X = ____ mm b) What is the value of R? R = ____mm (c) What are the UCLx and LCLx using 3-sigma? Upper Control Limit ( UCLx) = _____mm Lower Control Limit ( LCLx) = _____mm (d) What are the UCLR an LCLR using 3-sigma? Upper Control Limit ( UCLR) = ___mm Lower Control Limit (LCLR) = ____mm (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) = ____mm Lower Control Limit (LCLx) = ___mm
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 Bold x overbarx (mm) Range R (mm) 1 154.9154.9 4.04.0 2 151.2151.2 4.44.4 3 153.6153.6 3.93.9 4 155.5155.5 5.05.0 5 158.6158.6 4.3 a) What is the value of x? X = ____ mm b) What is the value of R? R = ____mm (c) What are the UCLx and LCLx using 3-sigma? Upper Control Limit ( UCLx) = _____mm Lower Control Limit ( LCLx) = _____mm (d) What are the UCLR an LCLR using 3-sigma? Upper Control Limit ( UCLR) = ___mm Lower Control Limit (LCLR) = ____mm (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) = ____mm Lower Control Limit (LCLx) = ___mm
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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 Bold x overbarx
(mm)
|
Range R
(mm)
|
|
1
|
154.9154.9
|
4.04.0
|
|
2
|
151.2151.2
|
4.44.4
|
|
3
|
153.6153.6
|
3.93.9
|
|
4
|
155.5155.5
|
5.05.0
|
|
5
|
158.6158.6
|
4.3
|
a) What is the value of x? X = ____ mm
b) What is the value of R?
R = ____mm
(c) What are the UCLx and LCLx using 3-sigma?
Upper Control Limit ( UCLx) = _____mm
Lower Control Limit ( LCLx) = _____mm
(d) What are the UCLR an LCLR using 3-sigma?
Upper Control Limit ( UCLR) = ___mm
Lower Control Limit (LCLR) = ____mm
(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) = ____mm
Lower Control Limit (LCLx) = ___mm
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