Biomathematical fatigue models

A biomathematical fatigue model is a mathematical method for estimating how tiring a work pattern is likely to be, based on factors such as shift timing, sleep opportunity, and how shifts fit together over time.

These models turn a roster into a modelled estimate of fatigue exposure. They are widely used in shift-based and safety-critical industries to support planning and review. A fatigue risk index (FRI) — including methods based on HSE RR446 — is one example of a tool built on a biomathematical model.

This page explains the concept in plain English. It is not legal advice and does not describe any single product.

What a biomathematical fatigue model is

Researchers have studied how sleep, the body clock, and time awake affect alertness. Biomathematical models draw on that research to produce a population-level estimate of likely fatigue for a given pattern of work.

In simple terms, a model takes structured information about when and how long people work, makes assumptions about likely sleep, and produces an output such as a Fatigue Index or Risk Index. See Fatigue Index vs Risk Index.

A model output is a modelled estimate of relative exposure — not a measurement of any individual worker’s tiredness.

Why shift timing, sleep, circadian rhythm and workload matter

Models reflect several well-established influences on fatigue:

Time of day — the body clock (circadian rhythm) means alertness naturally dips overnight and in the early hours. See timing and circadian effects in fatigue models.
Sleep opportunity — how much realistic chance a pattern leaves for sleep before and between duties.
Cumulative load — how fatigue can build across repeated shifts with limited recovery. See cumulative fatigue in models.
Workload and breaks — how demanding the work is and whether breaks are realistic. See workload, breaks and fatigue models.

Two duties of equal length can carry different modelled fatigue exposure because of these factors — for example a night duty following several early starts versus an isolated day shift.

How models are used in planning

Used appropriately, a biomathematical model can support review by helping organisations:

Compare roster options on a consistent basis before implementation
Identify shifts or sequences with higher modelled exposure
Consider the likely effect of a change (for example shortening a shift or adding a break) before making it
Contribute one line of evidence during incident review, alongside other factors

ORR guidance notes that such tools can help assess the likely level of fatigue from a working pattern and compare alternatives — but stresses that outputs should not be used in isolation.

How models differ from real-time alertness monitoring

A biomathematical model estimates fatigue from the schedule. It does not observe the person.

It is not a measure of real-time alertness — it does not know whether someone actually slept, is unwell, or feels drowsy right now.
It works from assumptions about typical sleep during off-duty periods, which may not hold for a given individual.

Real-time alertness monitoring is a different category of technology and is not what these planning models do. This site does not promote any monitoring product.

Why models support decisions but do not replace judgement

Model outputs are decision-support, not decisions. They should be interpreted with competent judgement because:

They are population-level estimates — individual factors vary (age, health, sleep, home circumstances).
A low output does not prove a shift is safe; a high output does not automatically mean work cannot proceed.
Thresholds or colour bands applied to outputs are organisational policy choices, not legal limits.

Models should sit within a wider fatigue risk assessment and fatigue risk management system (FRMS) — never as a standalone verdict. See limitations of fatigue models.

Examples of use

Roster planning — comparing two candidate rotations to see which produces lower modelled exposure before consulting workers. See roster design principles.
Reviewing demanding sequences — checking whether a run of consecutive shifts or repeated early starts stands out.
Supporting discussion — giving planners, safety teams, and worker representatives a common reference point for dialogue.

In each case the model informs a documented, competent decision — it does not make one.

References

RR446 — The development of a fatigue / risk index for shiftworkers — HSE research report (2006) underpinning UK fatigue index methods
Fatigue — HSE — fatigue as a hazard; tools support wider risk assessment
Managing shift work (HSG256) — shift work risk assessment and use of assessment tools
Managing rail staff fatigue — ORR — Appendix D: benefits and limitations of fatigue risk assessment tools (rail industry guidance)