Extreme value statistics and long-term marine pitting corrosion of steel

To derive the extreme value statistics for maximum depth of pits in pitting corrosion, it is conventional to use the Gumbel distribution. However, this has been shown recently to be not entirely appropriate. Modern pitting theory considers that the pit population consists of two major sub-populations, ‘stable pitting’ that can produce extreme depth pits in longer-term exposures, and ‘meta-stable’ pitting. It is not appropriate to mix these two different populations. Also, because of lack of sufficient data at any one exposure time, it is conventional to combine data from different exposure times. Unfortunately the pit depth growth relationship commonly used for this purpose does not accord with actual observations. The reason is that for longer-term exposures sulphate-reducing bacterial activity is the main corrosive agent. Under these conditions some plausible assumptions show that the Frechet extreme value distribution is more appropriate than Gumbel to represent the maximum pit depth. A simple example demonstrates that the difference in maximum pit depth predicted by these two distributions is considerable. This could have serious practical implications for predicting long-term pitting corrosion failure. Also, the question of coupon size to optimize the amount of stable pitting is discussed.