Page 149 - The Six Sigma Project Planner

The list is endless. In Six Sigma, data on these characteristics are called attribute data or
discrete data. Process capability and actual process and product performance must also
be determined for attribute characteristics. While the basic procedure is the same as that
used to determine process capability sigma level and actual performance for variables,
the calculations themselves are different.

Measuring Process Capability for Attributes Data
For an attribute CTx, a state of perfect statistical control is operationalized when the
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appropriate control charts (usually c, p, np, or U charts) indicate no special causes for
an extended period of time. This state describes the process capability for the attribute.
When this state exists, then the process capability is measured by using the process
mean for the attribute, assuming a 1.5σ shift. Since the control chart measures the
attribute directly, there is no need for table lookups to determine the DPMO levels.
As with CTx measures of variables data, complete statistical control is not common for
attribute data. If control charts are in statistical control for, say, 90% of the time, then the
process capability is usually approximated by dropping the out-of-control groups from
the calculations. However, this mathematical trick should not be done unless the causes
of the out-of-control conditions have been identified. This is especially important for
attribute data, because it may be that the special cause of better-than-normal performance
provides clues for process improvement.

Example
A company is concerned about the error rate of a particular type of billing statement it
sends to customers. A control chart of weekly errors per 1,000 bills indicates statistical
control for two quarters (26 weeks). The average of the control chart (a c-chart) is 7.5
errors per 1,000 bills. What are the process capability (DPMO) and sigma level?

Solution
Once statistical control has been achieved, the process average can be used to estimate
the DPMO level. The average of 7.5 errors per 1000 bills is equivalent to a DPMO level
of 7,500. Adjusting for the 1.5σ shift gives a process sigma level of 3.9.

Measuring Actual Process Performance for Variables Data
If the process does not show statistical control or if we must measure a CTx attribute
without knowledge of the production sequence, then we cannot determine the process
capability. However, we can still describe actual process performance for the attribute.
Actual process DPMO performance is measured by using the sample mean. Product or
process sigma levels are calculated assuming a 1.5σ shift. The calculations are identical
to those above, except the sample mean is not obtained from a control chart in statistical
control. I.e., it is not computed from subgroups in a time-ordered sequence.

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Six Sigma Handbook, Chapter 12.

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