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					             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
              increment of time and “y” is the measurement.
           Calculate the median value of the data set and draw that line on
              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                                          Even Number of Data Points
     1           N=7                                                    1        N=6
     2                                                                  3
     2           Median=N+1/2                                           4
     3                                                                  5       Median=The avg. of the
                 =7+1/2=4
     7                                                                  5       number that is N/2 and the
                 The median is the 4th
     11                                                                 8       next number in the series.
                 number in the
     12                                                                         =[4 (the third number in
                 series, which is 3
                                                                                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




                                                                                                                           2
        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.




                                                                                           3
   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                       Number of Consecutive
           Data Points on the Chart             Ascending or Descending Points
                                                   Indicating a Special Cause
                   5 to 8                                  5 or more
                   9 to 20                                 6 or more
                  21 to 100                                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.




                                                                                  4
  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       Lower   Upper            Useful       Lower   Upper
Observations   Limit   Limit          Observations   Limit   Limit
    15           4      12                29          10      20
    16           5      12                30          11      20
    17           5      13                31          11      21
    18           6      13                32          11      22
    19           6      14                33          11      22
    20           6      15                34          12      23
    21           7      15                35          13      23
    22           7      16                36          13      24
    23           8      16                37          13      25
    24           8      17                38          14      25
    25           9      17                39          14      26
    26           9      18                40          15      26
    27           9      19
    28          10      19




                                                                          5
     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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