X-bar and R chart

X-bar and R chart 
Displays a control chart for subgroup means (an X-bar chart) and a control chart for subgroup 
ranges (an R chart) in the same graph window. The X-bar chart is drawn in the upper half 
of the screen; the R chart in the lower half. Seeing both charts together allows you to track 
both the process level and process variation at the same time, as well as detect the
presence of special causes.

X-bar and R chart

X-bar and R charts are typically used to track the process level and process variation 
for samples of size 8 or less, while
X-bar and S charts are used for larger samples.

 By default, Minitab's X-bar and R chart bases the estimate of the process variation, σ, 
on the average of the subgroup ranges. You can also use a pooled standard deviation,
 or enter a historical value for σ.

To display an X-bar and R chart
1 Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar-R.
2 Do one of the following:
• If subgroups are in one or more columns, choose All observations for a chart are in 

one column, then enter one or more columns. In Subgroup sizes, enter a number or 
a column of subscripts.
• If subgroups are in rows, choose Observations for a subgroup are in one row of 

columns, then enter a series of columns.
3 If you like, use any dialog box options, then click OK.

Example of X-bar and R chart 
You work at an automobile engine assembly plant. One of the parts, a camshaft, 
must be 600 mm +2 mm long to meet engineering specifications. 
There has been a chronic problem with camshaft length being out of specification, which
causes poor-fitting assemblies, resulting in high scrap and rework rates. 

Your supervisor wants to run X-bar and R charts to monitor this characteristic, 
so for a month, you collect a total of 100 observations (20 samples of 5 camshafts each)
from all the camshafts used at the plant, and 100 observations from each of your suppliers. 

First you will look at camshafts produced by Supplier 2.

How to make x-bar and R chart
 1 Open the worksheet CAMSHAFT.MTW.

X-bar and R chart -1

2 Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar-R.

X-bar and R chart -2

3 Choose All observations for a chart are in one column, then enter Supp2.

X-bar and R chart -3

4 In Subgroup sizes, enter 5. Click OK.

X-bar and R chart -4

5.we will get to X-bar and R chart below.

X-bar and R chart -5
Interpreting the results
The center line on the X-bar chart is at 600.23, implying that your process is falling 

within the specification limits, but two of the points fall outside the control limits, 
implying an unstable process. The center line on the R chart, 3.890, is also
quite large considering the maximum allowable variation is +2 mm. 

There may be excess variability in your process.

Note: Test Results for Xbar Chart of Supp2
TEST 1. One point more than 3.00 standard deviations from center line.
Test Failed at points: 2, 14

                   * If graph is updated with new data, the results above may no
                   * longer be correct.

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