Let's get rid of the word Fatigue. It's too emotional, too scary, to 'at the limit', too individual, too open to contest via FRMS, etc.
It would seem to me that the root cause of this event is two fold. The preceding duties were very disruptive to sleep patterns. The longest duties were at the end of a tiring block. Daft. One root cause.
Then the 12.30 duty, which was the catalyst for this debacle, was planned at the limit with no buffer. For the past 35 years I've been hearing this cry from the troops: "why are the limits treated as the normal target?" This cry has been ignored by management & CAA's the world over.
Even the refused duty on the last day was a lengthy one, not a little jaunt around the houses. It was >11.00hr duty finishing after midnight and meaning another late bedtime.
It has been said by the FRMS 'experts' that the only way to counter sleep deprivation is long periods of sleep, not napping. Sleep deprivation is accumulative over a few days and can take more than one sleep period to recover; similar to jet lag. Rostering, being driven by the CFO, look at numbers & limits, not the reality of human/family behaviour. There is no way in reality that 12hrs from off duty - on duty will achieve 8 hours full & deep sleep in a family environment. It would need 15 hrs.
In late 80's I worked for a non UK outfit. Their roster rules were much better than my local (non-UK) ones. We were flying Scandanavia-USA & Africa. We were not tired. The minimum rest time was to be taken at home and there was 2hours allowed to travel to/from home. Each duty had a 'degree of difficulty' factor. This accounted for start time, end time, total duty time and any time changes. The rest time had a recovery factor that had to balance the factor of the previous duty. It was not necessarily the full rest after the duty; that was not always possible, but as the duty factors built up so did the required rest factoring. If there was a reduction in 'company' rest time, using FTL limits, then a credit was rolled over to the next rest period. The idea was to create a balance between work & social. It worked quite well for our limited network operation. It was an enlightened attitude. When I used to have my pre-JAA medical done by a national (non-UK) medical centre that did many more professions than pilots, the doctors said that a real ingredient of health is a good balance between work & social life. All my years in UK, and for a tight fisted small non-UK charter outfit, I never came across that attitude; indeed quite the opposite, no respect for family life at all.
In this day of earlies & lates, i.e. larks & owls, why are pilots not allowed to opt for one or the other. I'm lousy at earlies, certainly 5, especially in winter. Other guys much prefer them; yet in the safety conscious airlines they do not offer a fixed roster of one or the other. Thus some pilots are operating below par, and in winter you need to very sharp. There seems to be an attitude that pilots can not be seen to have any sway over operations and rostering. They will do what they are told and be grateful for it.
Vive la revolution.