A Method for Evaluating Exposure to Nitrous Oxides by Application of Lognormal Distribution
A Method for Evaluating Exposure to Nitrous Oxides by Application of Lognormal Distribution: S.S. Borjanovic, et al. Department of Work Physiology, Institute of Occupational Health “Dr Dragomir Karajovic”—A lognormal distribution adequately describes exposure to nitrous oxides in a work environment. The aim of this paper was to assign to the measured data a certain degree of variability which defines the interval in which real concentrations can be found with a given probability. Exposures may be evaluated by using estimates of the geometric mean (GM) and the geometric standard deviation (GSD), i.e. central value and dispersion index, to calculate the confidence interval (Cl) around the mean exposure and compare this interval to the occupational exposure limit. The concentration of nitrous oxides (114 random temporal measurements covering all three shifts, during 6 consecutive days) on coated electrode welding in a car manufacturing plant, was determined with colourimetric direct reading method. Statistical analysis (chi‐square and Kolmogorov‐Smirnov goodness of fit tests, lognormal and Gaussian distribution fitting and Q‐G plots) was performed. The distribution of the nitrous oxides concentration in the work environment studied closely resembled that of lognormal distribution. The geometric mean was 4.098 mg/m3, median 4.00 mg/m3, geometric standard deviation 1.829 and 95% confidence interval 3.66‐4.58 mg/m3. It is possible to apply the computed GSD for evaluation of exposure limits to nitrous oxides in any other work environment, even with only a few measurements.
Extreme Value Distribution
The shorthand X ∼ extreme value(α, β) is used to indicate that the random variable X has the extreme value distribution with positive scale parameter α and positive shape parameter β. An extreme value random variable X with parameters α and β has probability density function f (x) = (β/α)e x β−e xβ /α − ∞ < x < ∞. The extreme value distribution can be used to model water levels associated with floods and earthquake magnitudes. The probability density function with three different parameter settings is illustrated below.
A task-based statistical model of a worker's exposure distribution: Part II--Application to sampling strategy.
A task-based statistical model of a worker's exposure distribution for an airborne chemical toxicant is applied to estimating the long-term average exposure level, mu. The precision in estimation is represented by the variance of the sample estimator, denoted by Var[mu]. A traditional sampling strategy consists of integratively measuring the 8-hr time-weighted average exposure level on randomly selected workdays, and computing the sample mean; this strategy is termed "simple one-stage cluster sampling," where each 8-hr workday is a cluster of thirty-two 15-min periods. Three alternative strategies involving measurements of 15-min TWAs are examined: simple random sampling of 15-min periods, and stratified random sampling of 15-min periods with proportional allocation by task, and with optimum allocation by task. All four survey designs provide unbiased estimates of mu. However, for a fixed cost, the stratified sampling designs may provide a lower Var[mu] than simple one-stage cluster sampling for less work time monitored.