Alico Steel Inc. manufacturers steel tubes that are used in gas grills for residential customers. The tube's overall length is crucial to assure a proper fit, and this dimension has been targeted as an important dimension to be stabilized for the steel tube manufacturing process. Tubes are cut from rolls of steel tubing using a punch press. The tubes are measured using an operationally defined method and the table below summarizes the results. 10 samples have been collected. Within each sample, 6 tubes are measured.
|
Tube Length (in centimeters)
|
|
Sample
|
|
|
Number
|
X-bar
|
Range
|
|
1
|
12.56
|
0.35
|
|
2
|
13.3
|
0.5
|
|
3
|
12.76
|
0.32
|
|
4
|
11.93
|
0.44
|
|
5
|
12.43
|
0.91
|
|
6
|
12.91
|
0.42
|
|
7
|
12.9
|
0.29
|
|
8
|
13.03
|
0.58
|
|
9
|
12.7
|
0.21
|
|
10
|
12.75
|
0.11
|
Based on the information provided, answer the following questions.
1. What is X-bar-bar? Round your answer to two decimals.
2. What is R-bar? Round your answer to two decimals.
3. According to the control chart parameter table, what is A2? Round your answer to two decimals.
4. Using the answers you input in question 1, 2, and 3, what is the upper control limit of mean chart? Round your answer to two decimals.
5. Using the answers you input in question 1, 2, and 3, what is the lower control limit of mean chart? Round your answer to two decimals.
6. How many special cause variations do you identify from the mean chart? Round your answer to the nearest integer.
7. What is D4? Round your answers to two decimals if needed.
8. Using your answers for questions 2 and 7, what is the upper control limit of range chart?
9. What is the lower control limit of range chart? Round your answer to two decimals.