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Example - SPC on Regression Residuals

Notes and Considerations

There is a process at a manufacturing facility that takes a plastic tube that is closed at one end (the "tip") and open at the other end (the "base"), and that punches a small hole through the tube wall near the tip.  There is a drawing dimension that sets a specification for the hole-to-tip distance.

The datum used to locate the punched hole is based on the end of the tube opposite the tip.  Because the hole is placed by measuring from the base of the tube, and because a preceding process causes the plastic tubes to shrink non-uniformly, the hole-to-tip distance is affected by variation in the overall tube length, which - in turn - is affected by tube shrinkage (in length) during the prior manufacturing process.

An SPC chart (X-bar and R) was created for the hole-to-tip measurements.  Both the X-bar and R charts based on the raw data had special cause variation showing the process to not be in a state of statistical control. But the variation reflected in the SPC chart includes the variation in the tube length.

A regression model was created for the hole-to-tip distance (Y) vs. tube length (X).  Regression model assumptions were checked and the model seemed reasonable. A table of regression model residuals was then generated, and SPC charts were created based on these residuals. The SPC charts (X-bar and R) now show the process to be in a state of statistical control … if we account for variation in the overall length of the plastic tube.

What does this mean?

This means that the process and equipment is in a state of statistical control (is ‘stable’) when it comes to placing the hole in the tube wall, when we also account for the variation in the hole-to-tip dimension that is caused by variation in the length of the plastic tube.

The variation due to the tube length is still physically present in the dimension for the hole-to-tip distance.  But the process has the potential to be statistically in-control.

Improvement of the process outcome for hole-to-tip dimension will largely depend on finding a method to prevent the variation in overall tube length from affecting the location of the hole from the tube tip.

There was agreement going into the study that it made sense that there was a good chance that the variation in the overall tube length was a cause of the issues with lack of process stability for hole-to-tip placement.  But it was not known if this was the only problem. This study appears to show that no other issue exists, which narrows the scope of the corrective action.

Data Set

See the file "SPC on Regression Residuals.xls" attached below.

This data was adapted from the output of an actual industrial process.  The actual values were changed by both a shift and by the addition of a small random value.  But the outcome remains the same.

Analysis or Script File

See the file "SPC on Regression Residuals.stw" attached below.

The analysis proceeds in three stages:

Stage 1
  • Create an X-bar and R chart for the raw data.
Stage 2
  • Create a regression model with Y as "hole-to-tip (mm)" and X as "tube_length (mm)".
  • Check the assumptions of the regression model for validity.
  • Generate a table of residuals.  Add the original data to this table.
Stage 3
  • Create an X-bar and R chart from the regression model residuals.