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

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter14: Data Mining

Section14.2: Classification Methods

Problem 11P

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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

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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