guide to help you interpret runcharts in terms of random and non-random variation. using four rules to identify non-random variation

1. © ABCi 2019
What is a Runchart?
In contrast to data collected before and after a change,
runcharts enable you to assess the effectiveness of each
individual change or PDSA cycle in real-time and use this
information to build knowledge of what works and what
doesn’t. It enables you to evaluate whether you are
achieving your aim (outcome) or that your processes are
reliable. This guide will enable you to understand the
variation that lives within your runchart, interpret it
accurately in order for you to make the appropriate
conclusions.
See also ‘Creating Runcharts’ & ‘Using
Runcharts’ Skills for Improvement Guides
(2/3)
See ‘Creating Runcharts (1/3)’ for instructions to construct runcharts in Microsoft Excel, also for
further details around the components of a runchart, when you would use these and their benefits.
See ‘Using Runcharts (3/3)’ to understand how to use runcharts in practice, plotting new data and
recalculating your median to represent non-random variation in your data.
Why is understanding variation so important?
All systems exhibit variation, this may result from the many interactions or flaws that are built into the
system. It is important to understand the variation within your system as this will enable you to make
appropriate conclusions and decisions based on your data. Your runchart will demonstrate either
random or non-random variation or even both.
• Non-random variation is usually caused by a known factor. Something has changed in your process
that varies your data. Non-random variation means that your process has become unstable, meaning
that it is less predictable. When improving something, you will destabilise the current process and
demonstrate non-random variation in your data in the appropriate direction (e.g. reducing delays or
increasing compliance), you would want this improvement to be sustained and become stable.
In order to interpret the variation in your runchart, you need to understand four rules. Should your
data trigger one of these rules, your data is demonstrating non-random variation (see next page).
Should your data not trigger one of the rules, your data is demonstrating random variation (see
runchart above).
• Random variation is data that displays irregular or
erratic fluctuations, that are based on chance. This data
shows that your process is stable, not changing in any
way unless something is applied to change it. You decide
if you are happy with the stable process running at this
level or if it needs to improve.
Interpreting
Runcharts
(2/3)
ABC
improvement
iSkills for

2. © ABCi 2019
What are the runchart rules?
There are four rules to determine whether your runchart is exhibiting random or non-random variation.
If a rule is triggered, the data is demonstrating non-random variation.
A Shift - 6 or more data points above or below the
median. Given there is a 50% probability of a data
point being above or below the median (p = 0.016), it
is extremely unlikely that 6 in a row is due to luck.
Any data point falling on the median will not break a
shift, but will not be counted as part of the 6 to make
the shift.
A Trend - 5 or more points consecutively going up or
down. If two or more consecutive points are exactly
the same value, this is not enough to break the trend
but will not be counted as part of the 5 that makes up
the trend.
Too many or too few runs – A non-random pattern
may be signalled by too many or too few runs. A run
is the amount of times the line crosses the median
plus 1, or how many times the line is above or below
the median.
Of note, if there are too many runs, consider if the
data on the graph is from multiple processes, e.g. day
shift & night shift, or weekday & weekend.
 Count the number of data points on the runchart and look this up on the table on the next page.
Lookup the corresponding upper and lower limits for the number of runs.
 Count the number of runs, this is the number of times the line crosses beyond the median plus 1, or
the total number of times the line is either above or below the median.
 If the number of runs falls within the range between the lower and upper limit – this is random
variation.
 If the number of runs falls outside the range between the lower and upper limit – this is non-random
variation
 The graph above has 25 data points, looking this up on the table below, for the data to show random
variation there should be between 8 and 18 runs. There are 6 runs (line crossing the median) in the
graph above and because this falls outside the 8-18 range, this graph is exhibiting non-random
variation.

3. © ABCi 2019
Number
data points
on run chart
Lower limit
for number
of runs
Upper limit
for number
of runs
10 3 9
11 3 10
12 3 11
13 4 11
14 4 12
15 5 12
16 5 13
17 5 13
18 6 14
19 6 15
20 6 16
21 7 16
22 7 17
23 7 17
24 8 18
25 8 18
Number
data points
on run chart
Lower limit
for number
of runs
Upper limit
for number
of runs
26 9 19
27 10 19
28 10 20
29 10 20
30 11 21
31 11 22
32 11 23
33 12 23
34 12 24
35 12 24
36 13 25
37 13 25
38 14 26
39 14 26
40 15 27
An Astronomical Point –
 Anyone eyeballing the chart would agree that an
astronomical point is beyond the normal range
 Caution: Every data set will have a highest or
lowest point. This doesn’t mean that it is
astronomical