A run chart is a line chart of data plotted over time. In other words, a run chart graphically depicts the process performance or data values in time order. Viewing data over time gives a more accurate conclusion rather than just summary statistics.
A run chart is also known as a trend chart or a time series plot. Usually, run charts are used in the measure phase of the DMAIC project and it helps to identify trends or shifts in the process and allows testing for randomness in the process.
Difference between Run chart and control chart
Control charts are used to monitor the stability of the process. In other words, they measure any type of output variable over time. The goal is to see the results consistently fall within the control limits. On the control chart, both upper and control limits are defined. Typically, control limits are defined as three standard deviations from the mean. If the results fall within the control limits, then the process is stable; otherwise, it suggests that the process is not stable.
A run chart is similar to a control chart, but the key difference is it can reveal shifts and trends, not the process stability. Since the run chart does not have control limits, it cannot detect out-of-control conditions. However, it will graphically depict how the process is running. You can turn a run chart into a control chart by adding upper and lower control limits. A pattern or trend indicates the presence of special cause variation in the process.
Why use a run chart
A run chart is used to determine whether or not the central tendency of the process is changing. Following are a few reasons to use a run chart
- Easy to construct
- It does not require too many calculations or software’ for analysis.
- Easy to interpret the results
- Minimum statistical knowledge is sufficient to draw and interpret the chart
When to use run charts
- To visually depict how the process is performing
- Effectively track and communicate improvements (and determine success)
- To identify process variation and avoid unbiased actions
- Display outputs to look for stability or instability
Key components of Run Chart
- Time- series: the specific time period of the output (hours, days, weeks, months); plotted on the horizontal (X) axis
- Output: The data measurement from the completed process; plotted on the vertical (Y) axis
- Data points: output values plotted on the chart
- Median line: the line on the graph that shows the average of all the output measure.
Run chart interpretation rules
The following paragraphs are the run chart decision rules used to avoid inaccurate analysis and initiate appropriate improvement actions:
Shift: – Seven or eight values in succession above or below the median line is a shift. Do not consider the points that fall on the median line as they are not toward or against the shift. A shift indicates a dramatic change in the process.
Runs– Too many or too few runs in the data displayed on the chart. In other words, one or more consecutive points are all lying on the same side of the line. Ignore the points exactly on the line!
Clustering– Too few runs or groups of points in one or more areas of the plot. It indicates measurement or sampling problems.
Trend– Seven or more consecutive points are increasing or decreasing. A basic rule of thumb is when a run chart exhibits seven or eight points successively up or down, then a trend is clearly present in the data and needs process improvement. This rule does not care whether the consecutive points are above, below, or crossing the median.
Mixtures– Too many runs in a chart with absences of points near the median line.
Astronomical Point– Astronomical points occur when there is one value that is very different from the other data values on the chart. It would be a value that is highly unlikely to occur again and would appear as an outlier.
Counting Runs
A non-random pattern is signaled by too few or too many runs, or crossings of the median line. A run is a series of points in a row on one side of the median. In other words, one or more consecutive points are all lying on the same side of the line. If only chance is influencing the process being measured with a run chart, then there should be a regularity at which data points go above and below the median to satisfy this condition. Some points can fall exactly on the median line, which makes it hard to decide which run these points belong to. Hence, ignore if the value is exactly on the median line.
To apply the above-mentioned interpretation of the rules, we first need to identify the useful values/observations in the data set. This can be achieved by counting the number of runs and avoiding the values on the median line.
If you observe a greater or fewer number of runs than expected in the chart, that means there is a non-random pattern in the process. Swed and Eisenhart developed a chart in 1943 to determine the minimum and the maximum number of runs required for each data point to follow the random variation in the process. In other words, no special cause existed in the process.
How to create run chart
- Determine the data to be measured
- Obtain the data – collect a minimum of 10 to 15 data points in a time sequence.
- Plot a graph with a time sequence in the horizontal x-axis (like, hours, days, weeks) and a vertical y-axis with measuring variables.
- Plot the data values in a time sequence
- Compute the mean/median and draw a horizontal line in the graph
- Analyze the graph, and observe the trends and patterns to detect special cause variation in the process
Run Chart Excel Template
Unlock Additional Members-only Content!
To unlock additional content, please upgrade now to a full membership.
Upgrade to a Full Membership
If you are a member, you can log in here.
Example:
Draw and interpret the following weekly mobile charger rejection data using the run chart.
Solution
- Enter the weeks data in one column and quantity in next column
- Plot a graph with weeks in horizontal x-axis, and a vertical y-axis with quantity
- Compute median value for the quantity and draw horizontal axis
- Interpret the results: From week 10 to week 17, consecutive values are in an upward trend.
Benefits
- Easy to identify an early change in process and useful for analysis of the simple process.
- It is easy to draw and interpret the results
- Identify changes/ trends over time
- The run chart will depict the effects or results of the process improvements graphically.
Limitations
The formation of a run chart is based on the input values. It does not help identify unexpected or surprise events.
It cannot identify the stability of the process as it does not have control limits.
Every process will have some inherent variation. Often, normal process variation concludes that a trend or cycle exists in the process.
Helpful Videos
Other Helpful Links
-
Ted Hessing
I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams. Overtime I've grown the site to help tens of thousands of Six Sigma belt candidates prepare for their Green Belt & Black Belt exams. Go here to learn how to pass your Six Sigma exam the 1st time through!
View all posts
-
Ramana PV
View all posts
As someone deeply immersed in the realm of process improvement methodologies, particularly in the context of Six Sigma, I've not only studied but practically applied the principles discussed in the article on run charts. My experience extends beyond mere theoretical understanding, delving into real-world applications within the DMAIC (Define, Measure, Analyze, Improve, Control) framework. Allow me to guide you through the intricacies of run charts and their significance in process analysis.
Understanding Run Charts: A run chart is not just a graphical representation of data over time; it's a dynamic tool used to depict process performance or data values in chronological order. In the DMAIC project, particularly in the measure phase, run charts play a pivotal role. Identifying trends and shifts in the process, along with testing for randomness, are crucial aspects of their utility.
Distinguishing Run Charts from Control Charts: While control charts focus on monitoring the stability of a process by ensuring output variables consistently fall within control limits, run charts differ. The absence of control limits in run charts allows them to reveal shifts and trends, providing a visual narrative of how a process is running. Interestingly, you can convert a run chart into a control chart by introducing upper and lower control limits, helping identify special cause variations.
Why Use a Run Chart: Run charts are not just easy to construct but are also accessible for interpretation. Their utility lies in determining changes in the central tendency of a process. The simplicity in construction and interpretation, along with the minimal statistical knowledge required, makes them valuable tools in process improvement initiatives.
Key Components of Run Charts: Understanding the components of a run chart is fundamental. The time-series (X-axis), output (Y-axis), data points, and the median line are critical elements. The median line represents the average of all output measures.
Run Chart Interpretation Rules: The rules outlined in the article are guidelines for accurate analysis. Recognizing shifts, runs, clustering, trends, mixtures, and astronomical points aids in deciphering the data. The decision rules ensure that the analysis avoids inaccuracies and initiates appropriate improvement actions.
Counting Runs: Counting runs is a method to identify non-random patterns in the process. Deviations from the expected number of runs indicate a potential issue in the process that requires attention.
Creating a Run Chart: The step-by-step guide to creating a run chart involves obtaining data, plotting it over time, calculating mean/median, and drawing a horizontal line for analysis. The article provides a concise template for creating run charts using Excel.
Example and Benefits: An example of using a run chart to analyze weekly mobile charger rejection data illustrates practical application. The benefits include early identification of process changes, simplicity in drawing and interpreting results, and the ability to identify trends over time.
Limitations: Acknowledging the limitations of run charts is crucial. They may not identify unexpected events, and the absence of control limits makes them unable to determine process stability conclusively.
In conclusion, run charts are indispensable tools in the arsenal of process improvement professionals. Their simplicity, coupled with the ability to reveal trends and shifts, makes them valuable assets in the pursuit of operational excellence.
