You have selected your monitor to be representative of your population under every point of view that you could check, but you still feel it under-estimate consumption. You are not alone, and it is likely not your fault nor it is the monitor’s fault. It is just statistics.
The water industry (and the whole world) often uses mathematics based on the assumption that the data is normally distributed. We may do this unaware, but even when we are aware, the alternatives are much more complicated, so we end up approximating a normal distribution.
However, consumption is far from being normally distributed. A normal distribution is symmetric around its mean and has no limits on the possible values. Consumption distributions on the contrary are bounded in zero (we cannot have a negative consumption) and have long right tails, meaning that we often observe large outliers. Note that this applies to all components of consumption: day use, night use, household, commercial, leakage, etc.
This difference has consequences that influence your chances of picking a representative monitor. Why is that? An asymmetric, skewed distribution, like the ones describing consumption, has a mean that is different from the median. This results in the fact that, if you pick 100 different monitors, approximately 70 of them are likely to under-estimate consumption, while about 30 will significantly over-estimate consumption. Their average will tend to the correct population value, overall, but the problem is that in real life you don’t have 100 monitors, you have one. So, chances are that it will be underestimating consumption.
So, what can we do about it? There are multiple paths one can take, but diving into non-Gaussian statistics (studying non-normal distributions) is definitely not for everyone given its complexity, and often gets you stuck on the absence of mathematical solutions.
At Artesia we have successfully implemented a solution that approximately corrects for the assumption of normality in the data, so that we can continue applying mathematics based on normal distributions after the correction. This is based on using a log-normal distribution, which can easily be transformed to a normal distribution. The result is often an increased consumption estimation, but also a more realistic uncertainty estimation. While this is still an approximation, it significantly improves the representation of reality. You can see in the picture below how using a log-normal distribution represents a real monitor much better than a normal distribution with the same mean and variance as the data.
If you are curious about knowing more, you can contact us directly here, or you could join the Water Balance Working Group that Artesia is coordinating on behalf of many UK Water Companies. We can help improve your consumption estimations and will gladly discuss the best approach for you.
