Most examples of Xbar charts use raw data
that are grouped dynamically or by a specified
variable. The data values determine the group
mean, which is plotted on the chart. The center
line and control limits are also calculated
from the data. In some circumstances, the data
are already summarized into group means, ranges
and/or standard deviations. Summarized data
can be used in variable charts by selecting
appropriate options. This discussion will illustrate
how to generate Xbar, R and S charts using summarized
data.
The first example generates an Xbar and range
chart. The data are summarized for each lot.
The data needed to produce the chart are the
average diameters, range values, subgroup designations
and subgroup sizes. The dialogue to produce
the chart begins the same as a chart using raw
data. Within the Xbar chart dialogue, select
Avg_Diameter as the data variable, choose Subgroup
Size using a variable and select Units_Tested.
The important variation in this chart is to
select the Summarized Data button. Check the
box labeled Data are summarized and provide
the variable containing the ranges or standard
deviations. In this case, the subgroup sizes
are reasonably small, so we are going to use
the ranges in the Range variable. This dialog
is shown in Figure 1.
Figure 1
The control chart is displayed in Figure 2.
Since the subgroup sizes are not constant, the
control limits are not constant. Because of
this, adding the values of the control limits
to the chart do not provide helpful information.
A more useful alternative is to add variables
to the data tips. In this example, it is advantageous
to add the range, subgroup size (n), upper control
limit and lower control limit to the default
data tips for each point.
Figure 2
The accompanying R chart for this data requires
that the user check the Data are summarized
box under the Summarized Data button. An example
of this dialogue can be seen in Figure 3. It
is helpful to include the subgroup size and
control limits in the data tips for this chart
as well.
Figure 3
The resultant range chart is displayed in Figure
4.
Figure 4
The data set in the following example has larger
subgroup sizes. Instead of a variable with the
subgroup ranges, this dataset contains the subgroup
standard deviation as shown in Figure 5. When
entering the variable, there is no option to
specify the type of value being passed to the
control chart.
Figure 5
By default, control limits for X-bar charts
are calculated using subgroup range values.
However, the use of range values is valid as
long as the subgroup sizes are between 2 and
30, inclusive. This dataset uses the Units_Tested
variable for subgroup sizes. These values are
well beyond the allowable subgroup size. Attempting
to produce an X-bar with the current selections
would result in an error as shown in the example
in Figure 6. Note that this is basically the
same dialogue that was used to generate the
X-bar chart in Figure 3, even though this data
set has much larger subgroup sizes and sample
standard deviation values instead of the range
values. The software recognizes that the subgroup
sizes are not compatible with the choices that
have been made up to this point. It is, therefore,
necessary to specify that the control limits
be calculated using the subgroup standard deviations.
Figure 6
The flag to specify that the control limits
are to be calculated based on standard deviations
instead of ranges is found in the dialogue in
the Control Limits button. The dialogue is shown
in Figure 7.
Figure 7
As discussed in the previous series of charts,
the control limits vary. The subgroup sizes
and control limits are added to the plotted
data tips. The Xbar chart is displayed in Figure
8.
Figure 8
Generating the S chart uses similar choices
as the R chart. The user specifies the variable
containing the standard deviation values and
checks the summarized data box under the Summarized
Data button as illustrated in Figure 9.
Figure 9
The selection of additional data tip variables
produce the final S Chart in figure 10.
Figure 10
If you would like additional information, please
call our Support staff at (541) 752-4100 or
send email to
.
