Page 365 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 345

• 0 to 10 percent: Acceptable
• 10 to 30 percent: Marginal
• Over 30 percent: Unacceptable

Interpreting a Repeatability Control Chart
Repeatability control charts are constructed by grouping each appraiser’s trials
for each sample unit into a single subgroup. The size of the subgroup is equal
to the number of trials per sample unit. The variation within a subgroup is an
estimate of the repeatability error inherent to the measurement equipment so
long as the variation is shown to be statistically stable over all parts and all ap-
praisers. This assumption may be proved by observing the range chart for re-
peatability.
The range chart should be in statistical control (all the plotted groups within
the control limits). Each plotted group represents the variation observed
between the trials by a specific appraiser for a single sample unit. If a group is
out of control, the variation observed between the trials for that sample unit
was larger than expected (based on the variation observed for the other sample
unit). Perhaps the sample unit had an abnormality that impeded the measure-
ment. This suspicion grows if the out-of-control condition is observed for the
same sample unit in more than one appraiser’s measurements.
The X chart for repeatability is analyzed quite differently from most X
charts. The plotted statistic, X , is the average of each appraiser’s trials for a given
sample unit. These X variations are an indication of variation between sample
units. The control limits, however, are calculated using the average range between
trials for each sample unit, providing an indication of repeatability error. Since it

is desirable that the measurement system detect real differences between sample
units in the presence of this repeatability error, the subgroup-to-subgroup varia-
tion (i.e., sample unit fluctuations) should be larger than the repeatability error
(i.e., the control limits). Many subgroups should be out of control on the X chart
if repeatability is sufficiently small relative to process variation. AIAG recom-
mends that at least half the subgroups exceed the X control limits.
Repeatability control charts are available in two formats: combined and per
appraiser. The combined charts are those typically used to analyze statistical
stability of the measurement system across selected appraisers and parts. The
per-appraiser charts are provided to estimate each appraiser’s repeatability
independently. Appraisers’ repeatability then may be compared to indicate pos-
sible training benefits.