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# Calculate X-Bar-Bar, R-Bar

Scenario/Summary
1. A transmission manufacturing company has been having process difficulties at one its assembly stations. Thirty samples of 4 gears (n=4) have been selected from the process and are provided below.
Observations
Sample 1 2 3 4
1 4.92 4.26 4.94 4.29
2 4.65 5.54 5 5.42
3 5.77 5.26 4.76 4.79
4 6.25 4.88 5.66 4.44
5 5.27 5.41 6.02 4.91
6 5.22 5.38 5.08 4.65
7 5.47 4.68 4.56 4.7
8 5.71 4.54 4.17 4.87
9 5.24 5.58 4.72 5.41
10 4.42 5.18 4.79 4.73
11 5.14 4.26 4.71 5.48
12 4.92 5.78 5.5 5.05
13 5.79 3.83 4.3 4.78
14 4.92 4.8 4.75 5.59
15 5.68 5.74 4.65 5.2
16 5.43 4.81 5.27 4.96
17 4.79 6.04 4.47 5.18
18 4.43 5.08 4.69 6.43
19 5.35 5.95 5.29 5.89
20 5.03 4.66 5.25 4.46
21 5.32 5.09 5.57 5.91
22 4.3 4.47 3.27 4.34
23 6.07 4.97 5.51 5.02
24 5.11 4.9 5.91 4.66
25 4.5 5.24 4.86 4.35
26 4.91 4.79 5.74 5.03
27 4.65 4.71 4.81 5.32
28 4.7 5.5 6.04 4.3
29 5.87 5.3 5.78 5.07
30 4.41 4.75 4.95 5.11
2. Calculate X-Bar-Bar, R-Bar, and associated control limits using the data in the table above.
3. Create X-Bar•R (Average & Range) Control Charts from the data in table above.
4. Discuss notable out-of-control conditions displayed in the completed X-Bar•R (Average & Range) Control Charts. Only consider points outside the Control Limits. Do not consider runs, set of points within certain zones, etc.
5. If the conditions you note could be defined as assignable conditions and they are removed from the process, what will happen to the X-Bar•R Control Chart?
(a) Remove the data related to the out-of-control points you observed from the origainal data and recalculate a new X-Bar-Bar, R-Bar, and associated control limits.
(b) Create new X-Bar•R (Average & Range) Control Charts from your updated data.
6. Discuss how the two sets of Control Controls are different. What has changed?
Problem 1:
Calculate X-Bar-Bar, R-Bar, and associated control limits using the data in the table above and create X-Bar•R (Average & Range) Control Charts.