# 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).