in a paper (link) that was published in the proceedings of a 1978 statistics workshop the famous British statistician George Box wrote:
Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = nRT relating pressure P, volume V and temperature T of an "ideal" gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules. For such a model there is no need to ask the question "Is the model true?". If "truth" is to be the "whole truth" the answer must be "No". The only question of interest is "Is the model illuminating and useful?".
Box later wrote in his 1997 book, Statistical Control: By Monitoring and Feedback Adjustment (which was co-authored with Alberto Luceño):
It has been said that "all models are wrong but some models are useful." In other words, any model is at best a useful fiction—there never was, or ever will be, an exactly normal distribution or an exact linear relationship. Nevertheless, enormous progress has been made by entertaining such fictions and using them as approximations.
Putting this into context for bio-mathematical model usage for predicting fatigue in aviation, it is important to not over-rely on model output but instead take a conservative 'stance' addressing risk more broadly.
It is only too easy to fall into the trap of an inspect/re-work approach based on some made-up threshold by a model vendor meant to separate 'safe' from 'unsafe'. Please find here a high-level comparison between these inspect/re-work approaches and a process control approach that embrace model shortcomings. For more details on how to best use fatigue models throughout the crew management process, recognising they are flawed, look no further than to this document. Enjoy!