Question

a) what is the value of x?

b) what is the value of R?

c) what are the UCL(x) and LCL(x) using 3-sigma?

d) what are the UCL(R) and LCL(R) using 3-sigma?

e) if the true diameter mean should be 155 MM and you want this as your center normal line what are the new UCL(x) and LCL(x)?

Question Help Refer to Table S5.1 - Factors for Computing Control Chart Limits 3 sigma) 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 ked of 10 pistons produced each day, the mean and the range of this diameter have been as follows: SCO ts: Mean x Day mew 1 Range R (mm) 42 48 3.9 (mm) 1569 1532 1516 157.5 1546 2 3 4 5

Answer 1

# SAMPLE	AVERAGE	RANGE
1	156.9	4.2
2	153.2	4.8
3	151.6	3.9
4	157.5	4.8
5	154.6	4.7
AVERAGE	154.76	4.48

X-BAR = AVERAGE OF X VALUES = 154.76

R-BAR = AVERAGE OF R VALUES = 4.48

A2 VALUE CORRESPONDING TO N = 10 = 0.308

D3 & D4 VALUES CORRESPONDING TO N = 10, D3 = 0.223 & D4 = 1.777

FOR X

UCL = XBAR + (A2 * RBAR) = 154.76 + (0.308 * 4.48) = 156.14

LCL = XBAR - (A2 * RBAR) = 154.76 - (0.308 * 4.48) = 153.38

FOR R

UCL = RBAR * D4 = 4.48 * 1.777 = 7.96

LCL = RBAR * D3 = 4.48 * 0.223 = 1

E. IF X BAR = 155:

FOR X

UCL = XBAR + (A2 * RBAR) = 155 + (0.308 * 4.48) = 156.38

LCL = XBAR - (A2 * RBAR) = 155 - (0.308 * 4.48) = 153.62

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