Page 393 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 373

Interpretation

The run tests apply statistical tests to determine if there are any patterns or
trends in the plotted points. Run tests 1, 2, 3, 5, and 6 provide an indication
that the process mean has shifted, whereas the others tell us something about
sampling errors, inconsistent with the base premise of rational subgrouping.

Run test 4: An indication of sampling from a multistream process
(subgroups alternate between two or more process levels)
Run test 7: An indication of stratification in sampling (multistream
sampling within a subgroup)
Run test 8: An indication of sampling from a mixture (multistream
sampling, subgroups on each side of the center from separate
distributions)

The statistical basis of the run tests is simply that if the subgroups are truly
from the stated distribution and independent of one another, then there will
not be any pattern to the points. The run tests increase the power of the control
chart (the likelihood that shifts in the process are detected with each subgroup)
but also provide an increased (yet minimal) false-alarm rate.
Keep in mind that the subgroup that first violates the run test does not
always indicate when the process shift occurs. For example, when run test 2 is
violated, the shift may have occurred nine points (or more or less) prior to the
point that violated the run test. As another example, a process may be in con-
trol and not in violation of the run tests for a period of time, say, 50 subgroups.
Then the process average shifts upward. As more and more subgroups are
added at the new level, subgroups in the original 50 subgroups will start violat-
ing run tests or control limits because these points now show an unnatural

pattern relative to the combined distributions of the two process levels.

Scatter Diagrams

A scatter diagram is an XY plot used to investigate the correlation of one vari-
able with another.

When to Use

Analyze Stage

• To investigate the correlation of one variable with another