Using measurements of exposure from multiple tasks to reliably estimate full-shift exposures requires some decision making. For example, let’s say we have three tasks with exposure to crystalline silica. The three tasks have extensive, high quality survey data, and each task shows significant variability in short-term exposure limits (STELs) and in their impact on the estimated time-weighted average (TWA).

How do we most appropriately use those task survey data? Should we use the 95th upper percentile of the dataset for each task to calculate the TWA? Or should we use the median, arithmetic mean, or geometric mean of each?

This may not be a common dilemma in industrial hygiene, but many of us have needed to aggregate several sets of data to make a decision. If our decision involves only one input variable, the procedure is usually simple. But what happens when we have to put together multiple pieces to reach a decision, and each piece has uncertain or variable data? Which part of the data do you use?

Maybe you’re uncertain what the correct value should be. Do you use best- and worst-case calculations? How do you quantify the effect of your input choices on the results? How do you communicate the uncertainty and its ramifications?
VARIABILITY AND UNCERTAINTY
Usually, none of the data or information we work with is 100 percent certain. We usually have variable data, uncertain data, or both. Even a relatively reliable and certain input parameter, such as estimates of adult male or female body weight, will still show variability at different ends of the human range.

A great tool to use when we have variable or uncertain data is Monte Carlo simulation (MCS). MCS encompasses a versatile range of tools that are useful in IH calculations, especially when we work with variable or uncertain data. “Uncertainty” in the MCS context generally refers to something we know little about. The range of human susceptibility to a new chemical, for example, is truly uncertain.

MCS can be helpful when we use task-based data distributions to estimate total job exposures, or when we use mathematical models with known input parameter data distributions. With MCS, we can estimate the distribution of exposures for an individual or group. Perhaps the most common use of MCS so far in human health risk assessment has been to estimate the distribution of environmental exposures, such as children’s exposure to contaminated soil following a site soil remediation project.

The MCS technique IHs use most often involves assembling the statistical distributions of the various input values for our calculations. A calculation could involve a mathematical model, such as the one used to estimate the concentration of an air contaminant in a room. This equation at steady state conditions is rendered as

Making

Decisions
with Uncertain Data

Practical Examples of Monte Carlo Simulations

BY THOMAS W. ARMSTRONG