Run Charts
Understanding What They Are and How They Are Used
Dennis A. Ehrich, MD September 25, 2008
Creating a Run Chart
Hand-Drawing a Run Chart
Plot data points as a line graph on x-y axes, where “x” is the Calculate the median value of the data set and draw that line on
increment of time and “y” is the measurement.
the chart
Sort the data from smallest to largest value Count the data points. That count=N If “N” is an odd number: Median=N+1/2. Begin counting from
smallest to the largest number. When the count reaches N+1/2, that number is the median If “N” is an even number: Median=The average of N/2 and the next number in the series. Begin counting from smallest to the largest number. When the count reaches N/2, stop and take the average of that number and the next number in the series. That average is the median
Calculating the Median
Odd Number of Data Points 1 N=7 2 2 Median=N+1/2 3 =7+1/2=4 7 The median is the 4th 11 number in the 12 series, which is 3 Even Number of Data Points 1 N=6 3 4 Median=The avg. of the 5 number that is N/2 and the 5 next number in the series. 8 =[4 (the third number in the series) +5 (the next number in the series)] / 2=4.5
Balestracci, D., and Barlow, J, Quality Improvement. 1998 Center for Research in Ambulatory Health Care Administration
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Definitions
A run is 1 or more consecutive data points on the same side of the median line A useful observation is one that does not fall on the median line
•Sixteen of the eighteen observations are useful •There are 10 runs on this run chart
Four Tests for Special Cause Variation in a Run Chart
Testing for Special Cause Variation on a Run Chart
Test 1. Are any runs longer than expected? If so, then that run represents a special cause.
If there are fewer than 20 useful observations, then 7 or more
data points in a run indicate a special cause. If there are 20 or more useful observations, then 8 or more data points in a run indicate a special cause.
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Testing for Special Cause Variation on a Run Chart
Test 2. Is there a trend? A trend is an excessively long series of consecutive increases or decreases in the data.
Total Number of Data Points on the Chart 5 to 8 9 to 20 21 to 100
Number of Consecutive Ascending or Descending Points Indicating a Special Cause 5 or more 6 or more 7 or more
Applying Tests 1 and 2
Total number of data points=18 Number of useful observations=16 Test 1-Since there are < 20 useful observations it will take ≥ 7 data points in a run to cause a run to be “too long” defining special cause variation Test 2-Is there a trend? For 18 total data points, it will take ≥6 consecutive ascending or descending data points to define a trend.
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Testing for Special Cause Variation on a Run Chart
Test 3. Are there too few or too many runs in the data?
Determine the number of useful observations in your data set. Use the following table to determine whether the number of
runs in your data are within the expected range. If the number of runs is above or below the expected range, the data suggest special cause variation
Expected Number of Runs
Useful Observations 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Lower Limit 4 5 5 6 6 6 7 7 8 8 9 9 9 10 Upper Limit 12 12 13 13 14 15 15 16 16 17 17 18 19 19 Useful Observations 29 30 31 32 33 34 35 36 37 38 39 40 Lower Limit 10 11 11 11 11 12 13 13 13 14 14 15 Upper Limit 20 20 21 22 22 23 23 24 25 25 26 26
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Applying Test 3
Are there too many runs? Useful observations= 24. Number of runs= 8. Expected number of runs = 8-17. Therefore there is no evidence for special cause variation.
Testing for Special Cause Variation on a Run Chart
Test 4. Fourteen or more points alternating above and below the median line is a saw tooth pattern indicate a special cause.
KQC=Key Quality Characteristic
When this pattern is seen, it indicates either that two different processes are operating at the same time and have been measured together; in which case stratification of the data would be helpful. Or, it may indicate tampering
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