Not sure about a formula, but in the UK there is a .45 minute reduction for each and every sector.
This is based on CAA "medical" evidence that a crews ability to react is reduced the more sectors they do. This application seems to be UK specific as a lot of EU Airlines are not FDP limited until they do 3 sectors or more.
The UK CAA maintain this makes G reg operators "safer" than some of their EU counterparts who call do all and sundry,the Spanish being the worst....
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