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Extremal Types Theorem (EVA Theory)
Extreme Value Analysis (EVA) is based on the Extremal Types theorem, which states that if samples are taken from a well behaved, arbitrary probability distribution, the resulting extremes (min / max) can be approximated and parameterised by one of 3 Extreme Value distributions.
These distributions are called:
- Type I (Gumbel) - for unlimited data
- Type 2 (Frechet) - with a lower limit
- Type 3 (Weibull) - with an upper limit
The generalized extreme value (GEV) distribution (characterized by three parameters) was developed to combine the three families of extreme value distributions. Extrapolations can be done both in space and in time.
The GEV distribution is thus used to model the distribution of the maximum (or the minimum) of a number of samples and extrapolate this into the whole sample space. It is useful in predicting the chance that an extreme will occur.
Application to Heat Exchangers
The Extremal Types theorem is thus suitable to predict the maximum wall loss in a bundle of heat exchanger tubes, where the maximum wall loss (or minimum wall thickness) is measured for a sample of the HX tubes.
Taking the measurements - Warning
The sample must be representative for the whole system! It is very dangerous to have only data from an easily accessible part of a system and apply EVA to predict wall loss for other parts of the system with, possibly, harsher corrosion conditions. In this case a reliable inference about the corrosion extent will not be obtained.
The measurements must thus be taken from all parts of the system which is assumed to be homogeneous. If there is evidence that the system is not homogeneous, stratification is advised. To select appropriate areas, knowledge and experience are required.