Reeves Soft Drinks has decided to use an R-Chart to monitor the changes in the variability of their 12oz filling machine. The operations manager randomly samples 8 cans of cola and measures the amount of cola (in ounces) in each can at 14 successive time periods.
obs1
obs2
obs3
obs4
obs5
obs6
obs7
obs8
Sample Range
1
12.01
12.04
12.00
12.03
12.04
12.00
12.02
12.00
0.04
2
11.97
11.99
12.02
12.03
11.97
12.03
12.01
11.98
0.06
3
11.99
12.01
11.97
11.96
11.98
11.99
12.00
11.99
0.05
4
11.98
12.02
11.97
12.04
12.03
12.03
12.04
12.03
0.07
5
12.01
12.02
12.03
12.02
12.01
11.98
12.04
12.04
0.06
6
12.02
12.00
11.96
11.96
12.02
12.02
12.01
11.96
0.06
7
11.98
12.03
12.00
12.02
12.00
12.04
11.96
12.02
0.08
8
12.03
12.02
12.02
11.97
12.01
11.96
11.97
12.02
0.07
9
12.04
12.03
11.96
12.00
12.04
12.00
12.04
12.05
0.09
10
11.96
12.05
12.02
11.98
12.01
12.02
12.01
11.99
0.09
11
11.96
12.02
11.97
12.01
11.95
11.99
12.05
11.98
0.10
12
11.98
12.04
12.05
11.99
11.95
12.01
12.00
11.97
0.10
13
12.02
12.04
12.05
12.04
11.99
11.97
12.01
11.97
0.08
14
12.01
11.99
12.02
11.97
12.00
12.04
11.98
11.99
0.07
Step 1 of 7: What is the Center Line of the control chart? Round your answer to three decimal places.
Step 2 of 7: What is the Upper Control Limit? Round your answer to three decimal places.
Step 3 of 7: What is the Lower Control Limit? Round your answer to three decimal places.
Step 4 of 7: Use the following sample data, taken from the next time period, to determine if the process is "In Control" Or "Out of Control".
Observations: 12.01, 11.96, 12.02, 12.11, 11.97, 12.04, 11.96, 12.01, 12.01, 11.96, 12.02, 12.11, 11.97, 12.04, 11.96, 12.01
Sample Range: 0.15
Step 5 of 7: Use the following sample data, taken from the next time period, to determine if the process is "In Control" Or "Out of Control".
Observations: 11.96, 12.12, 12.03, 12.03, 12.04, 12, 12.04, 12.02, 11.96, 12.12, 12.03, 12.03, 12.04, 12, 12.04, 12.02
Sample Range: 0.16
Step 6 of 7: Use the following sample data, taken from the next time period, to determine if the process is "In Control" Or "Out of Control".
Observations: 11.97, 12.02, 12.01, 11.97, 11.97, 12.04, 11.99, 12.04, 11.97, 12.02, 12.01, 11.97, 11.97, 12.04, 11.99, 12.04
Sample Range: 0.07
Step 7 of 7: You, acting as the operations manager, have concluded that the process is "Out of Control". What is the probability that the process is really "In Control" and you have made a Type I Error? Round your answer to three decimal places.