‘Cusum’ is a charting technique which originated in the world of quality control, and was first applied to energy management in the 1980s. Like so much in monitoring and targeting it relies on having good estimates of expected consumption, and the term ‘cusum’ stands for ‘cumulative sum of deviation from expected consumption’.
Suppose you have a weekly* monitoring and targeting regime. Thinking about one individual stream of consumption, you will have actual and expected consumptions each week and they will differ. Sometimes the difference will be negative, sometimes positive, and the magnitude of the differences will vary. Now imagine what the cumulative sum of those differences will look like as time goes by. If there is no bias either way, the random positives and negatives will tend to cancel out and the cusum (for that’s what it is) will maintain an approximately constant value. This will manifest itself as a generally horizontal trend when plotted as a time-series graph.
Now imagine what happens if performance of the thing you are monitoring changes. This will introduce a bias in the differences between actual and expected consumption. If performance has got worse, the cusum trend will bend upwards; if there was an improvement, it bends downwards. Looking at a time-series chart of the cusum value will show you when past changes in performance occurred.
But it’s not just the dates of past changes that we are interested in. Cusum separates the history of performance into episodes of good and bad performance. By an ‘episode’ I mean a succession of weeks – say five or more – which appear to behave similarly. Analysing the ‘good’ episodes in isolation enables us to tune the formula for expected consumption so that in future we will always be assessing actual consumption against the best it could have been. In this way, cusum gives us tough-but-achievable targets backed by evidence. Conversely, analysing poor-performance episodes gives us evidence about the nature of any adverse behaviour, which is invaluable diagnostic information.