From The Ergoweb® Learning Center

An Equation to Predict Maximum Acceptable Efforts for Repetitive Tasks

Peter Budnick, PhD, CPE

Researcher Jim R. Potvin has proposed an equation that could have significant impact on the way ergonomists estimate risk for repetitive tasks. In the introduction to his article, Potvin reviews the data and methods ergonomists typically draw from to estimate risk associated with specific tasks. He notes that there are gaps in the knowledge base, and robust data for the effects of repetition in particular are elusive. In some cases, for example, a task is done so infrequently that the recommended forces and torques (also called moments) can be set close to the maximum voluntary effort for a single repetition. There are various sources for maximum strengths and maximum voluntary effort data, however, as a task becomes more repetitive, the acceptable levels of force and torque exertions are more difficult to predict. Researchers such as Snook et al have conducted a great deal of psychophysical research that provides ergonomists with databases of force and torque exposures for specific types of tasks (e.g., pushing/pulling a cart; lifting or lowering a box, etc.), but such studies are time consuming and expensive, and numerous gaps remain in the knowledge base.

In this study, Potvin set out to analyze the existing knowledge base to see if he could identify any generalizable patterns that could be expressed in the form of a predictive equation. He established strict criteria for the psychophysical studies he included in his meta analysis to ensure the integrity of the data and “apples-to-apples” (my words, not his) comparisons among the data sets, resulting in the inclusion of eight psychophysical studies of manual upper extremity tasks.

In his analysis Potvin focuses on several variables, defined as follows:

  • Maximum Acceptable Effort (MAE), the average maximum voluntary effort (MVE, in force or torque), where 1.0 represents 100% of the MVE; and
  • Duty Cycle (DC), the portion of a task cycle in which effort is exerted, where 1.0 represents 100% of the cycle.

So, for example, if I performed a task that required me to grip a tool for 5 seconds out of a task that repeats every 10 seconds, my F would be 6/minute, my DC would be 0.5, and my MVE would be whatever force or torque level I could safely sustain over an 8 hour work day under these conditions.

Potvin first tested a relationship between frequency (F), as in repetitions/minute, and MAE, finding that it was only able to explain roughly half of the variation in the data set (r2=0.49, p < 0.001, RMS error = 14.6%), meaning it really wasn’t a good predictor for MVE. DC, on the other hand, was found to estimate MVE fairly well, with an r2=0.87 (p < 0.0001, RMS error = 7.2%), in the form of the following non-linear equation:

MAE = 1 – [DC – 1/28,800]0.24

where 28,800 is the number of seconds in an 8 hour shift. He further simplified the equation to:

MAE = 1 – DC0.24

In this form, the MAE estimates remain strong, within 0.6% of the MVE for all DC > 0.0002 (~6 seconds of effort out of an 8 hour shift).


Potvin provides the following example to illustrate how practitioners might use the equation:

… [Researchers] Peebles and Norris (2003) measured an MVE strength of 70.0 +/- 15.0 N for females (31-50 yrs) pulling a 20 mm block with a chuck pinch. If DC = 0.25, then the equation predicts the MAE to be 0.283, and the MAF, for the average female in that age range, is predicted to be (0.283)x(70.0 N) = 19.81 N.

What this Means for Ergonomists

I was intrigued when I saw this article, because I’ve often wished for an equation with the power to predict acceptable forces or torques. You may recall that Ergoweb got its start by launching the first comprehensive set of computerized job analysis tools, the Ergoweb Enterprise™. Ergonomists, engineers, therapists, safety professionals and other ergonomics practitioners use the software to evaluate the level of risk for specific jobs and tasks, then perform “what-if” analysis to develop and present specific recommendations for improvements that will lower risk.

Many risk assessment methods have been proposed and applied over the years, but only some have been validated as reliable methods to predict risk, and only some have withstood the test of time in the marketplace. Ergoweb’s criteria for including a method in JET™ has always been simple: is there peer reviewed, scientific evidence to support the method; or, are there regulatory reasons to include a method? Our reasoning for strict inclusion criteria is also simple: If it hasn’t been proven, it doesn’t belong in a our toolbox. This strategy proved wise during the ongoing debate over ergonomics risk assessment, especially in light of the political claims that “ergonomics is junk science” that erupted in debates over workplace ergonomics regulation and enforcement in the USA. However, our experience has also shown that there are significant gaps in the ergonomics knowledge base, and practitioners are therefore often left making conclusions and recommendations based on a mix of evidence produced through tools like those in JET™ and professional experience and judgement. In short, we often deal with, and accept, a lack of certainty in our predictions and estimates. We have lots of data points in our knowledge base, but we don’t often have an equation that connects those dots and fills in those gaps. This new equation could prove an invaluable method to do so for force and torque exposures.

But perhaps the most important lesson I might take away from this equation is that repetition in and of itself is not necessarily where ergonomist should concentrate our concerns. Actually, I’ve felt this way for quite some time, which is why you will never hear me use terminology like ‘repetitive injury’, ‘repetitive motion injury’ (RMI), or ‘repetitive strain injury’ (RSI). Repetition is only one risk factor, and as more scientific studies are showing, it may not be the primary concern, and in some cases of little concern. Instead, it is the duration of the event that appears to be the key factor. If you’ve ever studied or used the Strain Index, for example, you will recall that it recognizes duration of exposure, the same as duty cycle in this equation, as a primary risk factor.

While frequency/repetition is an important factor to consider, the length of an exertion may outweigh it’s importance in risk assessment. DC, which combines duration and frequency/repetition into a single variable, according to this research, is a better measure when predicting acceptable task demands in the workplace.

Another interesting reflection that Potvin provides in his discussion is that a long-held belief that people can exert up to 15% of their maximum voluntary muscle effort for indefinite periods of time without significant injury or fatigue concerns may not be accurate. Citing the Rohmert curves as the source of this often applied “rule”, Potvin indicates his review of the data suggests that operating at 5% of one’s maximum may be a better recommendation for maximum, long duration exertions.


As with all scientific studies, there are limitations to the interpretation and application of this equation, including:

  • This equation was developed using data applicable to the upper extremities only, so may not translate well to other body regions.
  • Due to limitations in the original data sets, caution should be used when applying this equation to:
    • Jobs with DC’s > 0.90
    • Jobs with effort durations greater than 17 seconds
  • The equation is limited in its application to individual tasks and cannot be extrapolated for more complex conditions with multiple task elements
  • The current equation was developed using only female subject data (because male subject data is scarce)
  • Because other factors (e.g., extreme postures) may influence risk, this equation, which includes only the DC factor, may be inadequate


Jim R. Potvin, “Predicting Maximum Acceptable Efforts for Repetitive Tasks: An Equation Based on Duty Cycle,” Human Factors: The Journal of the Human Factors and Ergonomics Society, published online 2 December 2011, DOI: 10.1177/0018720811424269. Last downloaded 28 December 2011 from (subscription required).

Correction: In the original version of this article, the equation MAE = 1 – DC0.24 was incorrectly displayed as MAE = 1 – DC0.25. The article was updated to display the correct version of the equation, MAE = 1 – DC0.24, on May 16, 2014.

This article is reprinted, with permission, from The Ergonomics Report™, where it originally appeared on December 27, 2011.