Question

Abico 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	11.56	0.35
2	12.3	0.5
3	12.76	0.32
4	11.93	0.44
5	12.43	0.91
6	12.91	0.42
7	11.9	0.29
8	12.03	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)

Answer 1

Tube Length (in centimeters)
Sample Number	X-bar	Range
1	11.56	0.35
2	12.3	0.5
3	12.76	0.32
4	11.93	0.44
5	12.43	0.91
6	12.91	0.42
7	11.9	0.29
8	12.03	0.58
9	12.7	0.21
10	12.75	0.11
Total	123.27	4.13

1. X-bar-bar = Sum of X-bars / 10 = 123.27 / 10 = 12.33

2. R-bar = Sum of Range / 10 = 4.13 / 10 = 0.41

3. A2 for sample size , n (6)  = 0.48

4. UCL = X-bar-bar + R-bar * A2 = 12.33+0.48*0.41=12.53

5. LCL = X-bar-bar - R-bar * A2 = 12.33-0.48*0.41=12.13

6. Apart from Sample 2 and 5 , all samples are beyond control limits, hence answer =8

7. D4 for n (6) = 2.00

8. UCL of Range chart = 2 * 0.41 = 0.82

9.D3 = 0

LCL =D3 * R-bar = 0.00