Managing energy bills can difficult, especially if you live in a climate with four diverse seasons in a year, and you work for a company with fluctuations in equipment usage. The changing weather and work load makes it difficult to determine when the numbers are too high, or there is an actual reduction in usage. Typically, the manager or engineer makes a comparison of the current bill to last month and the same month last year. However, without some criteria, when should they get alarmed and concerned about the bill, or relax and feel that everything is going well?
Take a look at this chart. What do you see?
Most people would pick apart differences by month, noticing increases in February, August, November and December. However, you should also notice decreases in April, September and October. Turns out, the totals come out about the same each year, so we should have probably ignored these differences, and considered them just noise or random variation.
How much is too much? 1%? 5%? 20%? instead of relying on “gut feel,” let’s let the historical data and statistical analysis tell us. This will give us a better way to determine whether to leave things alone, or investigate.
Here are the key things you need to move forward:
1) History of bills (minimum of 12 months, preferably 36 months or more)
2) Prediction of bills in the future
The historical data shouldn’t be too difficult to gather, but having a prediction for the future bills might be more difficult. We recommend using heating and cooling degree days, or a statistical analysis technique like regression. If you don’t want to get that detailed yet, use the amount from the same time period last year as the prediction (like we did above).
Once you have a way to predict your future bills, we will want to compare our actual to our predicted, to see how far off we are each month.
The Cumulative Summation (CUSUM) chart is a method for detecting small shifts in data. We look at the difference between the actual and the predicted, and keep a running total, to see if the differences are moving further and further from zero over time. If there is no major change in the differences over time, we would expect the chart to hover around zero over time. If the actual bill is consistently lower than the predicted, then we should see the chart move further and further from zero. Let’s look at an example.
The chart above shows a two year period of energy usage for a company. The red color is the predicted amount of energy, and the blue color is the actual usage. It appears to differ from the predicted during the most recent 12 months, but not during every month (Feb and June). At what point do we get concerned?
The Difference column is simply the Actual – Predicted. The C+ column is the running total on the Difference column. For the first row, it will be equal to the difference, but for row 2, we take the previous value (8) and add it to -16, which is the difference between 340 and 356. The new C+ value is -8 (8 + -16). This technique for using a running total allows us to detect smaller shifts in the data.
To create the CUSUM chart, we simply plot the C+ values on a control chart.
If you scroll down to the last row in the data set, we have a total cumulative difference of 269 above the predicted. This chart clearly shows that our actual data is increasing above our predicted data over time.
At what value will we decide that the C+ value is too far away from zero? We apply statistical methodology to determine limits on either side of zero. These limits will tell us that the summed differences are too far away, so the prediction no longer matches the actual results.
The default setting for a CUSUM chart is to be able to detect a shift in the data of at least one standard deviation. The standard deviation is calculated from the original data (before you start tracking with the CUSUM chart). With a one standard deviation, we use a factor of 4.77 times the standard deviation to calculate the upper and lower CUSUM limits (or you can use 5 times, to keep it simple). For our data set, we calculate standard deviation from the data prior to these two years, which equates to 36. So we take 4.77 x 36 = 171.72. Therefore, if our C+ value goes above 171.72 or below -171.72, then our differences have varied too far from our predictions, and we need to figure out why. In our example, the month of July has a C+ of 173, so it goes beyond the limits.
If this was your electricity data, then you would be detecting electricity bills that are exceeding the predictions, and July would be the first month when you can confidently say that the results are not matching the predictions. In this case, it’s going above the predictions, so you would want to investigate why there is an increase in electricity usage throughout the year (not just during July, since this is a cumulative running total). The other issue could be that the predictions are not very accurate, which are underestimating the actual usage, so a new and improved model might be needed.
If you want to select a smaller or larger shift than one standard deviation, the table below can provide some help. In our example above, H represented 4.77, for a shift of one standard deviation. If you wanted to detect a shift of 1/2 of a standard deviation, then you would multiply your standard deviation by 8.01. This is a larger value, because it takes more data to ensure that a smaller shift has occurred.
This chart works even better when there is less variability between the months (for data that is less affected by weather and temperature), such as process equipment or server electricity usage. This will provide a smaller standard deviation between months, and therefore the limits will be tighter, and a small shift will be much more noticeable. Traditionally, those consistent processes might use Statistical Process Control (SPC) to monitor for trends and shifts in the data, however small shifts are difficult to detect with traditional Shewhart control charts. Contact us if you want to learn more about a combined Shewhart-CUSUM chart, which allow you to monitor for both small and large shifts in the data. There are also some more complex methods for CUSUM that we can provide more details on, if you are interested.
Want to try it out yourself? Download this Excel file for free…
Here are some other resources, if you want to read more about CUSUM charts…
- Using CUSUM charts with Degree Days predictions (from Carbon Trust, starting on pg. 9)
- CUSUM charts within Energy Monitoring and Targeting section (from Bureau of Energy Efficiency, starts on p. 179)
Has anyone used a CUSUM chart? What are your experiences with it? If you want to achieve your Certified Energy Manager (CEM) certification, you should try it out with your own data (the best way to learn), since CUSUM charts are part of the CEM Body of Knowledge.