Fujiyama Electronics Case Study

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The hardest part about this assignment is finding the center line. The center line is always X-bar-bar. (An x with two bars above it). It's the mean of all the sample means. I've attached an Excel spreadsheet showing how to calculate X-bar-bar. First, you find the average of each sampe. There were four in this case. The average is at the bottom. Then you take those four numbers and find the average for those. I rounded up to 5.1 to make it easier to graph. So X-bar-bar = 5.1.  

Once you X-bar-bar then, it all comes together.
For the first part, the center line (CL) is 5.100 and the CLR = 1.083. Then use the formula for the control limits:        ± A2   = 5.100 ± 0.729 (1.083) = 4.31 to 5.89  For the R-chart: UCLR = D4   = 2.282 (1.083) = 2.47

LCLR = D3  = 0
 
Once you construct the charts, look for anything unusual. Usually this will be something out of the control limits. In this case, there were a couple points that were. For your new chart, you need to remove those points from the data set and do the entire thing over again pretending that they weren't there. (Start from recalculating x-bar-bar. The easy way to do this is to just delete the lines of the points you want to eliminate. Remember to divide by the number of points you now have rather than the original 30. For example, if you pulled out two points, you would divide by 28 to get your average).  

New Center Lines: Center Line  = 5.037; CLR :  = 1.057
            Control limits for the chart are:
 
 ± A2   = 5.037 ± 0.729 (1.057) = 4.266 to 5.808
 
            For the new R-chart:  UCLR = D4   = 2.282 (1.057) = 2.412                                         LCLR = D3   = 0  Center Lines, CL : = 5.100; CLR : = 1.083
Control limits for the - chart are:

± A2 = 5.100 ± 0.729 (1.083) = 4.31 to 5.89
For the R-chart: UCLR = D4 = 2.282 (1.083) = 2.47
LCLR = D3 = 0

2.

X-bar Chart
4
4.5
5
5.5
6
6.5
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
Sample number
Averages
Averages
Lower control limit
Upper control limit
Center line

3. We can see from the above - chart that points 19 and 21 are out of control and the R-chart shows point 18 is out of control on the range. We obtain the following control limits and related charts after dropping these 3 points:

4a. New Center Lines: Center Lines, CL : = 5.037; CLR : = 1.057
Control limits for the - chart are:

± A2 = 5.037 ± 0.729 (1.057) = 4.266 to 5.808

For the R-chart: UCLR = D4 = 2.282 (1.057) = 2.412
LCLR = D3 = 0

4b.

New X-bar Chart
4
5
6
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Sample number
Averages
Averages
Lower control limit
Upper control limit
Center line

New R-Chart
0
0.5
1
1.5
2
2.5
3
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
Sample number
Ranges
Ranges
Lower control limit
Upper control limit
Center line

5. The and R-charts now show that the process is in control.
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