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What are the x overbar​-chart control limits when the machine is working​ properly?   Calculate the upper control limit of the x overbar​-chart Calculate the lower control limit of the x overbar​-chart. What are the R​-chart control limits when the machine is working​ properly?   Calculate the upper control limit of the ​R-chart. Calculate the lower control limit of the ​R-chart. The process is in control if all sample mean and range values are within the control limits. What seems to be​ happening? Has the process been in​ control? Yes or no?

What are the x overbar​-chart control limits when the machine is working​ properly?   Calculate the upper control limit of the x overbar​-chart Calculate the lower control limit of the x overbar​-chart. What are the R​-chart control limits when the machine is working​ properly?   Calculate the upper control limit of the ​R-chart. Calculate the lower control limit of the ​R-chart. The process is in control if all sample mean and range values are within the control limits. What seems to be​ happening? Has the process been in​ control? Yes or no?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question
Refer to the table
Factors for Computing Control Chart Limits (3 sigma)
LOADING...
for this problem.
 
Your​ supervisor, Lisa​ Lehmann, has asked that you report on the output of a machine on the factory floor. This machine is supposed to be producing optical lenses with a mean weight of 50 grams and a range of 3.5 grams. The following table contains the data for a sample size of
n=6
taken during the past 3​ hours:
                                                                                                                                                          
Sample
1
2
3
4
5
6
7
8
9
10
x
55
47
49
50
52
57
55
48
51
56
R
3
1
5
3
2
6
3
2
2
3
Part 2
Set the control limits for this process for the
x​-chart
when the machine is working properly.
 

a) What are the x overbar​-chart control limits when the machine is working​ properly?

 

Calculate the upper control limit of the x overbar​-chart

Calculate the lower control limit of the x overbar​-chart.

What are the R​-chart control limits when the machine is working​ properly?  

Calculate the upper control limit of the ​R-chart.

Calculate the lower control limit of the ​R-chart.

The process is in control if all sample mean and range values are within the control limits. What seems to be​ happening? Has the process been in​ control? Yes or no?

Data Table Sample Size, n 2 3 4 5 6 7 8 9 10 12 Mean Factor, A₂ 1.880 1.023 0 729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, DA 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1 777 1 716 A Lower Range, D3 0 0 0 0 0 0.076 0 136 0.184 0.223 0.284
Transcribed Image Text:Data Table Sample Size, n 2 3 4 5 6 7 8 9 10 12 Mean Factor, A₂ 1.880 1.023 0 729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, DA 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1 777 1 716 A Lower Range, D3 0 0 0 0 0 0.076 0 136 0.184 0.223 0.284
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