Personal Experiences of Statistics and Probablity in Corrosion Work

The main technical article in CM this month is about reliability analysis. I haven't read it yet but it probably encompasses extreme value statistics. This has propelled me into thinking about probability and in this month's TT article I will share some of my experiences particularly in relation to my own researches.

It's a subject I've been fascinated by since at least the early 70's - M J Maroney's 'Use and Abuse of Statistics' was THE book (when most people were reading Club magazine or NME, my bedtime reading was Maroney).

We all learnt at school that when you measure something in science there will be an error and "to have confidence" in the result, we need to know what that error is. (There are random errors and systematic errors but it is the former I will be mainly concentrating on here).

Early on in my PhD work I did some weight loss measurements on groups of three nominally identical steel samples, in identical solutions under identical conditions. I was not that surprised to find that the values varied, typically by a factor of about 30%. The values were added up, divided by three and the arithmetic mean (average) quoted (perhaps putting a range in, in brackets). OK so far. Next I started making resistance measurements on paints and my supervisor suggested that I made not 3 but 20 measurements. Why so many? I soon found out! Now the measurements were not 30% different but showed a 4, 5 or even 6 orders of magnitude variation between nominally identical areas! Luckily the results split into two groups creating a bimodal distribution, with ten or so values in each group.

The Standard Deviation of each group was calculated and because, even within one group, values showed scatter by up to two orders of magnitude, geometric mean (average of log values) rather than arithmetic mean was used. Then an average R (+/-) of the high group, and average R (+ / -) of low group were quoted. However another important (perhaps more important) value was the ratio No. of highs/ No. of lows in the set of 20.

So the next question that arose was "if one changed conditions (e.g. made the coating thicker) and found the high to low ratio had changed; when did a difference in this high to low ratio become significant?". This involved computation of the standard error (not too difficult an equation and one of three in my PhD thesis!). This has practical significance. Because the less protective/ weaker areas (low R) are small compared with the less weak (high R) areas, the more coats of paint you apply the less the chance of finding "overlap".

So if you know the high to low ratio for each coat of paint you should be able to calculate the number of coats of paint you would need to apply to be "fairly sure" that you didn't have a weak area.This will depend on the area: to have the same low (e.g. 1 %) chance of finding one in a square kilometre of painted surface compared with one square metre you will need more coats! Then I would recommend adding one extra coat for luck! (If I've lost you at this point, don't worry; many moons ago, in 1999,1 published a paper in CM about all this and copies are available.)

So this latter piece of work touches on reliability analysis and extreme value statistics. Also back at that time I remember helping a fellow research student who was trying to discover whether a certain inhibitor molecule was adsorbed more at grain boundaries than on the grains. Student's t test was used to prove they did although my contribution was mainly photographic(!).

When I hit the nuclear industry circa 1977, one of the first things I was asked to do was to analyse a lot of scattered data of iron metal loss against time (waterside corrosion loss). I was told to derive a correlation coefficient (R).This was done on a large Olivetti number crunching machine (pre computer days!). Then at the PRA it was back to paints where statistics reared its head (and still does) in fitting model circuits to real impedance (EIS) data (a figure called Chi squared was computed automatically and looking at that figure gave you an idea of how closely the data fitted the curve/ model).

Later I used statistical methods (Student's t again I think) to work out whether removing lead from electrocoat baths caused a significant decrease in corrosion protection (it did but it was small effect). In the last ten years though I have got involved with electrochemical noise measurements (ENM) and to get ANY useful information at all from electrochemical noise one HAS to apply statistical techniques. Some of them are relatively simple i.e. calculation of the Standard Deviation of the voltage noise and of the current noise (luckily all done by computer). If you then check whether the data set is Caussian (Normal), you can (with some degree of confidence but to WHAT degree is still uncertain!) calculate corrosion rates. Other techniques used in ENM work are a bit more complicated and I don't have space to cover them here!

Anyway, sorry if this has been a little dry but it is a subject I'm interested in. If anybody out there has corrosion or protection data and needs assistance in analysing it, I'm happy to help (my wife is also a statistician so if I get stuck.... !).The e-mail address is as usual douglas@harrbridge.freeserve.co.uk -PS. I will find something more photogenic to talk about in next month's column!