Task to TWA Estimation
Recently I have been thinking about how to incorporate uncertainty into task-based assessments. To estimate a full shift exposures from partial shift or task-based assessment you’d use the following equation:
Where each measured concentration is weighted by the duration of the exposure, and then averaged over the shift duration. Any part of the total shift duration not accounted for in the top half of the equation is assumed to have no exposure by default. This is great. It allows you to still get a full shift exposure (assuming you captured everything), but also lets you see which tasks are contributing the most to the overall exposure. However, we’d never rely on a single full-shift measurement to determine acceptable exposures, so should we be collecting many task-based samples and accounting for that in the TWA calculation?
Simple Example
A boilermaker performs three different welding processes. We collect a measurement of each process and ask / observe how long each process takes in an average day. Using the data tabled below, we get a full-shift time weight average of 0.53mg/m3. If we wanted to control exposures (assuming we could only pick one process), we look to the concentration*time to see that process 2 will give us the best return for effort despite having the lowest concentration.
Uncertain Example
Of course, things change day to day. If we instead took multiple samples from each of the welding processes, and a record of task durations, we could account for this variability in our estimation of the time weight average. Basically, instead of using single numbers in the TWA equation, we use distributions. In this example, the concentrations are log normally distributed and the times are normally distributed. Using the data in the table below we could simulate 10,000 estimated time weighted averages to pull even more insight out of the assessment.
The simulated data can then be plotted as a histogram:
Analysing the simulated data gives some interesting insights:
Our new expected TWA concentration is: 0.64 mg/m3
The probability of an exceedance of 1 mg/m3 is 10%
The control priority is the same as the simple example, but now process 2 is a much bigger contributor relative to the simple example.
The assumptions you make about the distributions of exposures and time will effect your estimated TWAs.
Here is my R code if you want to have a play.
What do you think?