Alico Steel Inc. manufacturers steel tubes that are used in gas grills for resid
ID: 3271015 • Letter: A
Question
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. For example, if your answer is 11.2364, input 11.24. Your answer is . (1 point)
2. What is R-bar? Round your answer to two decimals. For example, if your answer is 0.2364, input 0.24. Your answer is . (1 point)
3. According to the control chart parameter table, what is A2? Round your answer to two decimals. For example, if your answer is 11.2364, input 11.24. Your answer is . (1 point)
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. For example, if your answer is 11.2364, input 11.24. Your answer is . (1 point)
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. For example, if your answer is 11.2364, input 11.24. Your answer is . (1 point)
6. How many special cause variations do you identify from the mean chart? Round your answer to the nearest integer. Your answer is . (1 point)
7. What is D4? Round your answers to two decimals if needed. Your answer is . ( 1 point)
8. Using your answers for questions 2 and 7, what is the upper control limit of range chart? Round your answer to two decimals. For example, if your answer is 11.2364, input 11.24. Your answer is . (1 point)
9. What is the lower control limit of range chart? Round your answer to two decimals. For example, if your answer is 11.2364, input 11.24. Your answer is . (1 point)
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
Explanation / Answer
1) in industrialstatistics,the x-bar-bar chart is atype of Shewhart control chart that is used to monitor the arithmetic means of successive samples of size n,This type of control chart is used for characteristics that can be measured on a continuous scale such as weight,temperarure,thickness etc.
control limit of x-bar-bar chart
Uper limit=process mean +A2*R-bar
central limit=x-bar-bar
lower limit=process mean-A2*R-bar
Total of x-bar-bar=114.84
Mean of x-bar=11.49
2) In statistical quality control the R chart is a type of control chart used to monitor variables data when samplesare collected at regular intervals from a business or industrial process.
R-bar=sum(max-min)/ number of observation
control limit of R chat
upper limit=D4*R-bar
central limit=R-bar
lower limit=D3*R-bar
Total of R=4.13
R-bar=0.41
3) A2 is constant value which is calculated from table
Here A2=0.30
4) upper control limit for mean chart
=process mean+A2*R-bar
=11.48+0.30*4.13
=12.72
5) lower control limit for mean chart
process mean-A2*Rbar
=11.48-0.30*4.13
=10.24
6) Average of the observation identify the mean chart
which is here 11.48
7)D4 which is constant value andcalculated from table value
here D4 is 1.79
8) upper control limit for R chart
=D4*R-bar
=1.79*4.13
=7.39
9) lower limit for R chart
=D3*R-bar
0.22*4.13
0.91
here D3 is table value
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