Example of X and R chart
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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 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.

1    Open the worksheet CAMSHAFT.MTW.

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

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

4    In Subgroup sizes, enter 5. Click OK.

Session window output

Xbar-R Chart of Supp2

 

 

 

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

 

* WARNING * If graph is updated with new data, the results above may no

          * longer be correct.

Graph window output

 

Interpreting the results

The center line on the X 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, 3.72, is also quite large considering the maximum allowable variation is +2 mm. There may be excess variability in your process.