### From a very clever colleague.

Been pondering ND’s table of return periods required for different exposure periods.

The question relates to what return period should be used to assess an ‘ offshore asset’ left partially complete over the northern hemisphere winter.

If you start off with the assumption that the accepted risk for marine ops is based on the use of the 10-yr return seasonal or monthly data for an exposure period of 30 days then that means there’s a probability of 0.1, 10%, that that event will occur on one day that month (the probability being the reciprocal of the return period). So that’s why you can reduce the return period to 1-yr if you’re only exposed for 3 days: the probability increases to 1 for the month but you’re only there for 3 days not 30 so the probability of that one bad day being in your 3 is 10% and that gets you back to a risk of 10%. This all assumes blind statistics, i.e. you can’t see out the window or a forecast.

Going the other way, for longer exposure, the use of the 10-yr return, all year, for up to a year exposure (as stated in ND) seems to me to entail the same risk if the extreme event happens in one month only. For example, if December is the month when the biggest storm happens then that won’t happen in August (usually !) so you can use the 10-yr, all year value for 6 or more months and there’ll still only be a 10% risk of ever seeing it. This argument seems to fall down when looking at the XXXX metocean data: the 10-yr, all year Hs is 14.2 m but from the monthly extremes it’s 14.2 m for Oct, Nov, Dec, Jan, Feb and March. So if you were only there in December, say, you’d use the 10-yr Dec data and there’d be a 10% chance of seeing it. But as you’re going to be there all winter there’s a 10% chance every month that you’ll see the same Hs. To my simple mind that means there’s a 6 x 10% chance that you’ll see it once in those 6 months. But that can’t be right because looking at the whole year there’s only a 10% chance that the 10-yr event will happen once in 1 year. So that’s the first question.

ND’s logic also looks strained when they say that for exposure periods of more than 1 year you should use the 50-yr return data. So for an exposure period of a year and a day, even if that day is in June, you go from the 10-yr return to the 50-yr return ? Now obviously p = 1 – ((T-1)/T)^n where p is the probability of failure in n years, T is the design return period and n is the exposure period. So for a design value of the 10-yr return and 1 year exposure the probability of failure is 0.1. Using ND’s table and an exposure of 2 years, say, you’d need the 50-yr data and you’d get a probability of only 0.04. If you were to use the 50-yr data for our case you’d have a probability of failure of only 0.02 so it would be much more conservative that using the 10-yr values.

It might be worth noting that according to BS 19902, DNV, etc., you only need to design the platform using the 100-yr data so with an exposure period of 25 years you have a probability of seeing that 100-yr event of 0.22 over the whole lifetime, double the probability that XXXX are proposing for seeing their 10-yr event this winter.

*Indeed, it’s got us confused for sure. Very interesting thoughts though. He’s a bright chap that one.*