Statistics for Process Control Engineers

13Extreme Value Analysis

When fitting a distribution to process data, by definition, there are relatively few values that lie in the tail(s). As a result there is less confidence that the fitted distribution truly represents behaviour in these regions. The overall fit may appear good but, if we wish to determine the probability of the process operating at the extreme(s), a more reliable approach should be adopted. This technique is known as extreme value analysis (EVA) which was developed from extreme value theory (EVT). It allows assessment of the probability of events being more extreme than previously observed. It is used when events have a low frequency but high severity.

We will use as an example the variation in the LPG splitter reflux flow. On any column reflux is a key manipulated variable, often automatically adjusted to maintain product composition or, in some cases, reflux drum level. Its value will vary in response to any type of disturbance to the column. The data comprise 5,000 measurements collected hourly. We saw in Section 10.2 that they appear to be normally distributed. We want to assess the probability of a very high reflux flow – perhaps because it is known to cause column flooding.

There are two methods of identifying which of the values should be classed as extreme. The first is to choose the highest value in a defined time period. Known as the period maxima (or sometimes the block maxima), in this example, we have chosen the highest value that occurs ...