Run Chart
The run chart is the most basic tool used to display how a process
performs over time. It is a line graph of data points plotted in a chronological
order, that is, the sequence in which process events occurred. These
data points represent measurements, counts, or percentages of process
output. Run charts are used to assess and achieve process stability
by highlighting signals of special causes of variation.
Why should teams use run charts?
Using run charts can help you determine whether your process is stable
(free of special causes), consistent, and predictable. Unlike other
tools, such as pareto charts or histograms, run charts display data
in the sequence in which they occurred. This enables you to visualize
how your process is performing and helps you to detect signals of special
causes of variation.
A run chart also allows you to present some simple statistics related
to the process:
| Median: |
The middle value of the data presented.
You will use it as the centerline on your run chart. |
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| Range: |
The difference between the largest and smallest values in the
data.
You will use it in constructing the Y-axis of your run chart. |
You can benefit from using a run chart whenever you need a graphical
tool to help you:
- understand variation in process performance so you can improve it;
- analyze data for patterns that are not easily seen in tables or
spreadsheets;
- monitor process performance over time to detect signal of changes;
and
- communicate how a process performed during a specific time period.
What are the parts of a run chart?
As you can see in Viewgraph 1, a run chart is made up of seven (7)
parts:
- Title: The title briefly describes the information
displayed in the run chart.
- Vertical or y-axis: This axis is a scale,
which shows the magnitude of the measurements represented by the data.
- Horizontal or x-axis: This axis shows
when the data were collected. It always represents the sequence in
which the events of the process occurred.
- Data Points: Each point represents an individual
measurement.
- Centerline: The line drawn at the median value
on the y-axis.
- Legend: Additional information that documents how
and when the data were collected should be entered as the legend.
- Data Table: This is the sequential listing of the
data being charted.
How is a run chart constructed?
| Step 1 |
List the data.
List the data you have collected in the sequence in which it occurred. |
| Step 2 |
Order the data and determine the range
(Viewgraph 2).
To order the data, list it from the lowest value to the highest.
Determine the range (the difference between the highest and lowest
values). |
| Step 3 |
Calculate the median (Viewgraph 2).
Once the data have been listed from the lowest to the highest value,
count off the data points and determine the middle point in the
list of measurements — the point that divides the series of
data in half. |
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• |
If the count is an odd number, the middle is an odd
number with an equal number of points on either side of it. If you
have nine (9) measurements, for example, the median is the fifth
value. |
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• |
If the count is an even number, average the two middle measurements
to determine the median value. For example, for ten (10) measurements,
the median is the average of the fifth and sixth values. To determine
the average, just add them together and divide by two (2). |
| Step 4 |
Construct the y-axis.
Center the y-axis at the median. Make the y-axis
scale 1.5 to 2 times the range. |
| Step 5 |
Draw the centerline.
Draw a horizontal line at the median value and label it
as the centerline with its value. The median is used as the centerline,
rather than the mean, to neutralize the effect of any very large
or very small values. |
| Step 6 |
Construct the x-axis.
Draw the x-axis 2 to 3 times as long as the y-axis
to provide enough space for plotting all of the data points. Enter
all relevant measurements and use the full width of the x-axis. |
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|
Note: One of the strengths of a run
chart is its readability, so don’t risk making it harder to
interpret by putting too many measurements on one (1) sheet. If
you have more than 40 measurements, consider continuing the chart
on another page. |
| Step 7 |
Plot the data points and connect them with
straight lines. |
| Step 8 |
Provide a title and a legend.
Give the chart a title that identifies the process you are investigating
and compose a legend that tells: |
| |
• The period of time when the data were collected
• The location where the data were collected
• The
person or team who collected the data |
How do we interpret a run chart?
Interpreting a run chart requires you to apply some of the theories
of variation. You are looking for trends, runs, or cycles that indicate
the presence of special causes. But before we examine those features
of run charts, a word about variation. Expect to see it. Just remember
that process improvement activities are expected to produce positive
results, and these sometimes cause trends or runs, so the presence of
special causes of variation is not always a bad sign.
- A trend signals a special cause when there is a
sequence of seven (7) or more data points steadily increasing with
no change in direction. When a value repeats, the trend stops. The
example in Viewgraph 3 shows a decreasing trend in lower back injuries,
possibly resulting from a new “Stretch and Flex” exercise
program.
When a run chart shows seven (7) or more consecutive ascending
or descending data points, it is a signal that a special cause
may be at work and the trend must be investigated.
- A run consists of two (2) or more consecutive data
points on one side of the centerline. A run that signals a special
cause is one that shows nine (9) or more consecutive data points on
one side of the centerline. In the example in Viewgraph 4, you can
see such a run occurring between March 15 and 28. Investigation revealed
that new software was responsible for the increase in duplication.
This was corrected on March 29 with the introduction of software “patch”.
Whenever data point touches or crosses the centerline, a run stops
and a new one starts.
When your run chart shows nine (9) or more consecutive data
points on one side of the centerline, it is an unusual event and
should always be investigated.
- A cycle, or repeating pattern, is the third indication
of a possible special cause. A cycle must be interpreted in the context
of the process that produced it. In the example in Viewgraph 5, a
housing office charted data on personnel moving out of base housing
during a 4-year period and determined that there was an annual cycle.
Looking at the 1992-1993 data, it is evident that there were peaks
during the summer months and valleys during the winter months. Clearly,
understanding the underlying reasons why a cycle occurred in your
process enables you to predict process results more accurately.
A cycle must recur at least eight (8) times before it can be
interpreted as a signal of a special cause variation. When interpreting
a cycle, remember that trends or runs might also be present, signaling
other special causes of variation.
Note: The absence of signals of special causes does
not necessarily mean that a process is stable. Dr. Walter Shewhart
suggested that a minimum of 100 observations without a signal
is required before you can say that a process is in statistical
control.
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