Calculate X-Bar-Bar, R-Bar

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.

Solution:
1. Using the template provided, click on the “Data and calculation” tab. In the upper left corner enter “30” for the number of samples and enter “4” for the sample size.

 

 
2. Enter the data into the yellow data area. Note: You will have to rotate your data to fit this table. When you are done you should have 30 observations (30 columns ), each with four results.

 

3. The template does all the calculations and plotting. The calculations are grouped into two parts, one for Averages (top group) and one for Ranges (bottom group). The X-Bar-Bar number we want in the top set of resultstitled “Center.” X-Bar-Bar = 5.057. The “Center” result the bottom set of data is R-Bar. R-Bar = 1.069.

 

3. Click on the “x-bar chart” tab to view the X-Bar Chart and you should see a chart that looks like the one below. (It’s called a X-Bar chart because you plot averages or X-bar’s on it.) We can see one point, point #22,is below the Lower Control Limit (LCL).

 
4. Click on the “R-chart” tab to view the R-Chart and you should see a chart that looks like the one below. No points outside the Control Limits can be seen.

 
5. We now have enough information to answer Questions 12, 2, & 3 in the case study.

 

Problem 2:
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? Calculate new X-Bar-Bar, R-Bar, and associated control limits, and create a new X-Bar•R (Average & Range) Control Charts.

Solution:
1. Click on the “Data and calculations” tab. Point #22 was noted as being out-of-control. Highlight the data results (4 numbers) under #22 and press delete on your keyboard.

 
2. Highlight all the data for points 23 though 30. Right click and select copy and paste the data into the top blank cell under #22.

 
3. Delete the four data points under #30 by highlighting them and pressing delete on your keyboard. You new data table should look like the following.

 
4. In the upper left corner change number of samples from “30” to “29.” If you forget to do this the Control Limit calculations will not be correct. Do not change the sample size.
6. Your new Means and Control Limits have been recalculated and are:

 
7. . Click on the “x-bar chart” tab to view the X-Bar Chart and you should see a chart that looks like the one below. No points outside the Control Limits can be seen.

8. Click on the “R-chart” tab to view the R-Chart and you should see a chart that looks like the one below. No points outside the Control Limits can be seen.

 
9. We have a enough information to complete steps 4 a & b.

Problem 3:
How are two sets of Control Charts different. What has changed?

Solution:
1. First, the most obvious observation we can make is that when we remove Point #22 the new Control Chart does not have any out-of-control points.

2. With the removal of Point #22 we can see the new X-Bar-Bar has increased, while the new R-Bar has decreased.

3. We can also see the Control Limits on the new X-Bar and R Charts have changed as well. The Control Limits for the X-Bar Chart have come tighter, which should not surprise us, since we removed the point that was outside the Lower Control Limit. No changes occurred to the Control Limits of the Range Chart.

4. We have now have enough information to produce the Word document to complete the project.
1. Calculate X-Bar-Bar, R-Bar, and associated control limits using the data in the table above.
2. Create X-Bar•R (Average & Range) Control Charts from the data in the table above.
3. 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, and so forth.
4. If the conditions you note could be defined as assignable conditions, and they are removed from the process, then 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 original data, and recalculate new X-Bar-Bar, R-Bar, and associated control limits.
b. Create new X-Bar•R (Average & Range) Control Charts from your updated data.
5. Discuss how the two sets of Control Charts are different. What has changed?