Etcetera Case

1
Etcetera Case

• X-Bar Chart
• R-Chart

2
Sample Size? Number of Samples?
Enter the data as shown. What is n? nnumber of
observations in a sample (order). Thus, n4. If
you use the wrong value for n in your exam, you
will receive no partial credit for all work done
on the problem.
3
Compute the sample means (X-bar column) and the
sample ranges (Range column). You take the
average and the range of each sample (order).
If you take the wrong averages in the exam, you
will receive no partial credit for all work done
on the problem.
Use Excel function AVERAGE() to take the
average. Use Excel functions MAX() and MIN() to
find the maximum and minimum, respectively. The
range is MAX()-MIN().
4
Equations for the X-bar Chart
The average of the sample means (cell F32) is the
center line of the x-bar chart. Enter this value
in Column H (the same value for the entire
column). The average of the sample ranges is in
cell G34. This is R-bar.
Look up Table 10.2 (reproduced in next slide),
find the values of A2, D3, and D4 corresponding
to n. Compute the UCL and LCL of the x-bar
chart, and enter the values in Column I and J,
respectively (the same value for the entire
column).
5
N 4 A2 0.73 D3 0 D4 2.28 If you pick the
wrong values in the exam, you will receive no
partial credit for all work done on the problem.
6
Equations for the R-Chart
The average of the sample ranges (cell G34) is
R-Bar. Add a column (Column K) and enter this
value. Compute the UCL and LCL of the R-bar
chart, and enter the values in Column L and M,
respectively (the same values for the entire
column).
7
Make 2 Copies of the Worksheet

• Now you are ready to plot.
• Click Edit, Choose Move or Copy Sheet.
• Repeat to make another copy of the worksheet.

Make sure the Create a copy box is checked.
8
Plotting the x-Bar Chart
9
Use the first copy of the worksheet to plot the
x-Bar Chart.Select and hide Columns B through E
as shown.
10
Select and hide Column G as shown.
11
Select A6J31 (shown as highlighted cells)Click
Insert and choose Chart.
12
On the Chart Wizard, choose XY(Scatter) as
shown.Click Press and Hold to View Sample to
preview.
13
Click Next.Then click Next again.
Note The Series in columns.
14
Choose Bottom for the placement of the
legend.Before you click next, experiment on
the other options.
15
Click Next. Choose Place chart as new sheet.
Name the new sheet x-Bar Chart as shown.
16
Notice that all points are inside the limits.If
one or more points are outside, you have to
discard them and collect more data.
17
Plotting the R-Chart
18
Use the second copy of the worksheet to plot the
R-Chart.Select and hide Columns B through F as
shown.
19
Select and hide Columns H through J as shown.
20
Select A6M31 (shown as highlighted cells)Click
Insert, choose Chart, and select XY(Scatter).
21
Click Next. Then click Next again. Choose
Bottom for the placement of the legend.
22
Click Next. Choose Place chart as new sheet.
Name the new sheet R- Chart as shown.
23
Notice that all points are inside the limits.If
one or more points are outside, you have to
discard them and collect more data.
24
Now you are ready to use the charts to monitor
your process.
25
The following day, we collected 10 samples
Note Data is not shown in the Etcetera Case.
Is the process in control?
26
Compute the sample means (column F).
The process is out-of-control if a sample mean is
outside of the x-Bar chart limits. The limits
were determined earlier, i,e., CL
30.40309 UCL 34.733855 LCL 26.072324 The
limits are shown here in columns G, H, and I.
27
Hide Columns B to E
28
Choose, Insert-Chart
29
Note The Series in columns.
30
A point is above the upper control limit
31
The process is out of control.

• One point (the 6th) is above the upper control
  limit.

32
Suppose all points are inside the limits of the
x-Bar Chart.

• Then you have to see if the sample ranges are all
  inside the limits of the R-Chart.

33
Compute the sample ranges (column F). For
example, F2MAX(B2E2)-MIN(B2E2)
The process is out-of-control if a sample range
is outside of the R-chart limits. The limits
were determined earlier, i,e., CL
5.932555 UCL 13.5262259 LCL 0 The limits
are shown here in columns G, H, and I.
34
Hide Columns B to E
35
Choose, Insert-Chart
36
Note The Series in columns.
37
The process is out-of-control.