T20-06 - 1

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T20-06 Control Chart (with Runs Tests)
Purpose Allows the analyst create and analyze a
"Control Chart". A visual analysis of the
control time series with upper and lower
confidence limits is shown along with the A/B
and U/D "runs tests" for randomness.
Inputs Observed Sample Statistics (range,
means, proportions, or defects per unit)
Control Chart Centerline, LCL, and
UCL Outputs Control Chart Runs Tests
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Run Charts Check For Randomness
Used in conjunction with control charts to test
for randomness of observational data. The
presence of patterns in the data or trends
indicates that non-random (assignable) variation
is present. A run is a sequence of observations
with a certain characteristic. Two useful run
tests . Runs above and below the centerline
data translated into A (above) and B
(below) . Runs up and down data translated
into U (up) and D (down)
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Counting A/B Runs
Counting Above/Below Runs
(7 runs)
B1
A2
A2
A4
A6
A6
B3
B5
B5
B5
B7
If a value is equal to the centerline, the A/B
rating is different from the last A/B rating.
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Counting U/D Runs
Counting Up/Down Runs
(8 runs)
U1
D6
U7
U7
U5
U3
U1
D4
D2
D8
Note the first value does not receive a notation
If two values are equal, the U/D rating is
different from the last U/D rating.
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Expected Number of Runs
Once the runs are counted they must be compared
to the expected number of runs in a completely
random series. The expected number of runs and
the standard deviation of the expected number of
runs are computed by the following formula
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Compare Observed Runs to Expected Runs
Next, we compare the observed number of runs to
the expected number of runs by calculating the
following Standard Normal Z-statistic
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Runs Test - In or Out of Control
For a degree of confidence of 99.7 (3 standard
deviations), we compare the comparison to -3
standard deviations and 3 standard deviations.
. If either the Zab or Zud is
.. lt lower limit (-3) then we have too few runs
(Out of Control) .. Between the lower
limit (-3) and upper limit (3) then we have
an acceptable number of runs (In Control)
.. gt upper limit (3) then we have too
many runs (Out of Conrtrol)
Acceptable number Runs
Too Few Runs
Too Many Runs
-3.00
3.00
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Example
The observed means of 20 samples each containing
5 observations are shown here. The Centerline
3.4995, LCL 3.4849, and UCL 3.5141 have been
calculated Create the Control Chart and conduct
the A/B, U/D Runs Tests for randomness.
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Input the Centerline, LCL, UCL, and Observed
Values for the appropriate control chart in the
light green cells.
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Input the Control Chart is automatically
displayed showing the Centerline, LCL, UCL, and
Observed Values
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Input the Sigma Level and the A/B and U/D Runs
Tests are automatically calculated.