The Informative Run Chart
One of the very first plots of a string of data is a simple run chart. The plot of the data over time. This plot provides information related to location, trends, patterns, anomalies, and more. A rather informative chart.
You have most likely constructed many run charts and if not, you really should. This short introduction to run charts will cover creating and interpreting them, as well as a few cautions and tips, as well.
When to Build a Run Chart
A run chart is designed to work with a single variable of data that has an association with a time sequence. For example, if measuring nail cut length of nails as they come out of the cutting machine in sequence. Another example would be the monthly water consumption for a household.
On the other hand, if making the same measurement of a random collection of nails that are found in a bin and they are not organized by moment of manufacture, then we have a single variable, yet the time sequence element is lost.
Therefore, when the data variable is collected or organized in a time sequence, then a run chart is a suitable choice to view the data.
How to Create a Run Chart
After collecting the data, check that the data is listed in time order. I’m going to plot the monthly water use (I record the water meter reading on the first of each month – I know that month lengths vary a bit, yet I can remember to check on the first of each month). The readings are listed by month and then calculate the monthly use by taking the difference in sequential months readings.
In my data set, the first three readings are 511.11, 514.99, 518.41. Therefore starting the second month we can determine the previous month’s use, 514.99 – 511.11 = 3.88. The next month’s use is 518.41 – 514.99 = 3.42. We have almost 5 years of data.
Since my data is in Excel, just highlight the data column and select View | Insert | Scatter Plot (I’m using just the simple plot using dots – you could also connect the dots, if desired.
In R, assign the data to a variable, x <- c(3.88, 3.42, … ). Then plot that variable, plot(x). You could also plot the data directly plot(c(3.88, 3.42, … )), if you’d like.
Remember to add a title, axis labels, etc.
Interpreting the Chart Well
On first look, does the chart make sense? Any clerical errors or mistakes in the dataset? Second, what do you and others know about the process being measured? Do the patterns revealed in the plot make sense with what is known about the process.
In the monthly water use run chart, the first 20 months seem rather consistent between 1 and 4 units of water. Then there seems to be annual spikes in water use. Well, we installed a large vegetable garden and landscaping all around the house – and we did a lot more outdoor watering.
I’m sure you noticed the change in use, the magnitude of the change, that it increases in water use was on an annual cycle, and that overall water use is increasing.
Sometimes, the run chart will reveal patterns that you did not notice before. Thus, this simple chart and help you learn more about the process being measured.
Cautions and Tips
Be aware of the time order or sequencing of the data. If I am interested in nail cut length and use a box of 100 nails from the hardware store, we may learn about the mean and variance, yet will not have meaningful information about changes or patterns due to changes over time-related to the cutting machine.
Yet, we record the nail cut length in the sequence of being measured from the box, we may find a time sequence pattern related to our measurement system, given the nails in the box are in random order related to the sequence of manufacture.
While creating a run chart is easy, it is informative related to a time sequence, therefore be cautious during data collection and recording to preserve the time sequence information.
A run chart is not a control chart, yet it does provide some information related to stability, trends, and so on. To determine process stability a run chart may be considered a quick look, yet a control chart is the appropriate plot and process to determine stability.
Finally, keep in mind that a run chart may appear to show a trend or pattern, yet it may be due to random fluctuation. Always compare what you see in the plot with what is know (or can be verified) about the process being measured.
Run charts are one of the 7 Basic Quality Tools (on some lists) and should be a routine tool you employ when examining a time-sequenced variable.