The overall average on a process you are attempting to monitor is 55.0 units. The process population standard deviation is 1.84. Sample size is given to be 16. ​a) Determine the ​3-sigma x​-chart control limits.   Upper Control Limit ​(UCLx​)=56.3856.38 units ​(round your response to two decimal​ places). Lower Control Limit ​(LCLx​)=53.6253.62 units ​(round your response to two decimal​ places). ​b) Now determine the ​2-sigma x​-chart control limits.   Upper Control Limit ​(UCLx​)=? units ​(round your response to two decimal​ places).

Question
1. The overall average on a process you are attempting to monitor is
55.0
units. The process population standard deviation is
1.84.
Sample size is given to be
16.
​a) Determine the ​3-sigma
x​-chart
control limits.
 
Upper Control Limit
​(UCLx​)=56.3856.38
units ​(round your response to two decimal​ places).
Lower Control Limit
​(LCLx​)=53.6253.62
units ​(round your response to two decimal​ places).
​b) Now determine the ​2-sigma
x​-chart
control limits.
 
Upper Control Limit
​(UCLx​)=?
units ​(round your response to two decimal​ places).
 
 
 
2. 
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
​Thirty-five samples of size
7
each were taken from a​ fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results​ were: Overall mean​ =
60.75
​lb.; Average range
R
​=
1.64
lb.
 
​a) For the given sample​ size,
the
control limits for ​3-sigma
x
chart ​are:
Upper Control Limit
​(UCLx​)
​=
61.43761.437
lb. ​(round your response to three decimal​ places).
Lower Control Limit
​(LCLx​)
​=?
lb. ​(round your response to three decimal​ places).
 
 
 
3.
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
Ross Hopkins is attempting to monitor a filling process that has an overall average of
725
mL.
The average range
R
is
6
mL.
 
For a sample size of
10​,
the
control limits for ​3-sigma
x
chart​ are:
Upper Control Limit
​(UCLx​)
​=
726.828726.828
mL
​(round your response to three decimal​ places).
Lower Control Limit
​(LCLx​)
​=?
mL
​(round your response to three decimal​ places).
 
 

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