Using biomathematical models in an FRMS reduces risk, improves production, and lowers cost.


By Tim Smithies and Dr Ian Dunican

It is important to remember that effective fatigue management within an organisation requires a systematic approach referred to as a Fatigue Risk Management System (FRMS). An FRMS should complement the broader Safety Management System and define and guide an organisation to systematically evaluate, manage and mitigate fatigue-related risk. An FRMS has several key aspects, including but not limited to:

  • Identification and assessment of potential fatigue hazards and risks.
  • Comprehensive fatigue monitoring is underpinned by ongoing data collection and analysis.
  • Continuous assessment of the effectiveness of the fatigue mitigation strategies.
  • Ongoing allocation of resources to address operational fatigue hazards and risks, including appropriate fatigue management training for all relevant staff

A common approach to identifying and assessing potential fatigue hazards and risks is biomathematical modelling in conjunction with safety and cost modelling.

What are biomathematical models?

Biomathematical models (BMM) are statistical models. They combine information on working hours with human biology (sleep/wake) to predict past, present or future fatigue or alertness levels. These models leverage many decades of scientific research into how our biology governs our alertness and sleepiness. At the core of BMMs is the well-understood and validated two-process model (Borbély, 1982), which specifies that ‘sleep homeostasis’ or homeostatic drive (process S) and the ‘circadian rhythm’ (process C) interact to determine our sleep drive as well as our wakefulness during the day.

  • Process S is simply a ‘pressure’ that builds over time awake (typically during the day) which is relieved with time asleep (typically at night).
  • Process C (circadian rhythm) is a daily rhythm that runs independently from Process S.


It is influenced by external factors such as the timing and properties of light exposure and meal and exercise timing (known as Zeitgebers). It is governed by the Suprachiasmatic Nucleus (SCN), which controls melatonin secretion in the pineal gland, and can be thought of as the human ‘body clock’. Sometimes, BMMs will incorporate other processes or fatigue-related components (i.e., ‘sleep inertia’ or process W). However, processes S and C form the backbone of BMMs.

How are they used? What benefits can they provide in an FRMS?

The use of BMMs can help predict past, present, and future risks of fatigue. The primary use of a BMM is to support the safe design of a shift and roster schedule by minimising risk or to as low as reasonably practicable (ALARP). They can also estimate fatigue risk that may have been present in an incident as part of a safety investigation. In addition, they can help identify fatigue risk timepoints within a given schedule or roster, for example, the 2nd night shift at 05:15 am. This information can then compare proposed or existing roster schedules for risk prevalence. They are also helpful for scenario planning for additional shifts and hours before or after a shift (overtime).

At Melius Consulting, with our clients or in research activities, we use these biomathematical models to support fatigue risk management system design, diagnostics and improvements.


Case Study

Melius Consulting supported Metro Trains Melbourne, Rolling Stock Division through rigorous scientific and industry research to quantify the fatigue risk using scientific principles, biomathematical modelling and operational experience. This reduced the inherent risk of roster design by >30%, a standard team-based roster across depots, and the ability to manage overtime and enable training and education, resulting in a cost saving of $3m.

Dave Carlton, General Manager, Metro Trains Melbourne

Research case study

Digging for data: How sleep is losing out to roster design, sleep disorders, and lifestyle factors. The health of fly-in fly-out (FIFO) workers is impacted by their employment roster. These shiftworkers can suffer sleep disorders and a drop in mental alertness – factors that contribute to safety levels on the job and at home. In the below infographic, the measure of alertness is derived from the biomathematical model and depicts risk (0-100%) across each shift. Measures of alertness <70% result in impairment.

It is imperative to understand that BMMs are not a substitute for a sound FRMS with a well-defined objective, clearly outlined workplace fatigue processes, indicators of compliance/ improvement, and a strategy to promote employee education/ buy-in to the fatigue management strategy. As stated by the Australian Civil Aviation Safety Authority (CASA),

“FRMS should be designed as comprehensive, multi-layered systems, in which biomathematical models, when used, provide a supporting role”.

Along similar lines, BMMs typically do not incorporate the effect of fatigue countermeasures such as caffeine or strategic light exposure. Instead, BMMs predict fatigue, given a particular schedule or sleep/ wake behaviour. Due to these factors, it’s essential that a BMM output is not interpreted as a precise and definitive measure of fatigue (and hence used as a ‘go/no go’ tool with cut-off values for activities/ operations is not recommended) and is instead considered as one piece of evidence or information alongside workplace experience and other FRMS when ultimately making decisions.

Melius Consulting supports business in determining risk associated with rosters using biomathematical modelling and the design and improvement of fatigue risk management systems. We have undertaken such work in mining for Rio Tinto, BHP, Whitehaven and in Oil and Gas for Woodside, Fugro and in agriculture with CBH Group, in rail with Metro Trains Melbourne, and numerous other applications.

Contact us today to discuss risk and cost reduction strategies.

Dr Ian Dunican or



  • Australian Civil Aviation Safety Authority. (2014). CASA Biomathematical Fatigue Models Guidance Document Summary.
  • Borbély, A. A. (1982). A two-process model of sleep regulation. Human Neurobiology, 1(3), 195-204.
  • Tabak, B., & Raslear, T. G. (2010). Procedures for validation and calibration of human fatigue models: The Fatigue Audit InterDyne tool.


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