Question

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

1010

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	156.9156.9	4.24.2
2	153.2153.2	4.64.6
3	153.6153.6	4.14.1
4	155.5155.5	5.05.0
5	156.6156.6	4.54.5

​a) What is the value of

x double overbarx​?

x double overbarxequals=___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).

Enter your answer in each of the answer boxes.

Answer 1

Answer a and b:

R= Max- Min	X-bar= average of sample
4.20	156.90
4.60	153.20
4.10	153.60
5.00	155.50
4.50	156.60
4.48	155.16
R-bar (Average of above values)	X-bar-bar (average of above values)

Answer c: D4, D3 and A2 are taken from table of factors computing 3 sigma control limits, sample size=10

A2 (n=10)			0.308
control limits for X bar,
CL or Xbarbar			155.16
UCL=Xbarbar+ (A2)*Rbar			156.54
LCL=Xbarbar- (A2)*Rbar			153.78

Answer d:

D4 (n=10)=			1.777
D3 (n=10)=			0.223
control limits for Range,
CL or R-bar=			4.48
UCL=R-bar*D4			7.96
LCL=R-bar*D3			1.00