Chemical Engineering June 2015 - 61

grouping allows for confident prediction
that the next sample taken
for worker 094 will likely be close to
these values. However, the broader
range of the exposure groupings for
the second worker opens the door
to the possibility that the next value
could be very high. This is problematic,
as we will soon see.
Interpreting exposure data
Now that both the GM and GSD
for the two workers are known, we
can find any value from within the
respective distribution by calculating
a percentile statistic according
to the following:
(6)
The product of the geometric mean
and geometric standard deviation
raised to the power of the z-score
for the desired percentile will result
in a comparison statistic that can be
used to assess risk [5]. We look in
the standard normal z-table and see
that the 95th percentile corresponds
to a z-score of 1.645. Plugging in the
GM, GSD and z-score for the grouping
of samples for worker 094 gives
a value for the 95th percentile statistic
of 6.9 mg/m3. We do the same
for worker 0152 and get a 95thpercentile
statistic of 21.7 mg/m3
[Editor's note: for exact values, see
footnotes for Table 1]. These two values
are compared to the Exposure
Categorization Scheme proposed by
the American Industrial Hygiene Association
(AIHA) [7] and further developed
by Hewett [5] (Table 2).
For the current example, we are
interested in the PEL for aluminum
total dust, which is 15 mg/m3. Applying
this value to the recommended
statistical interpretation column gives
us Table 3.
Exposures seen by worker 094 are
relatively low and close together, resulting
in the 95th percentile decision
statistic of 6.9 and thus the exposure
category of 2, " well controlled, few
exposures at low concentrations, "
provides adequate qualification.
Those of worker 0152 are low and
close together, with one significant
exception (at 13). This single high
value causes a much higher 95th
percentile decision statistic of 21.7
for these lognormally distributed
data. This value is well above the
PEL of 15, and thus we could say
the exposure is " poorly controlled. "
It is notable that the lower mean
exposure seen by worker 0152 (GM
= 3.7) has the higher GSD (2.9), and
thus has a much higher 95th percentile
statistic. This is because it is associated
with the broader range of values.
The highest of these, 13 mg/m3,
may look like an outlier in comparison
with the others in this exposure
group. Instead, this value is a true
measure of the worker's exposure to
aluminum dust on the day it was collected
and serves as an indicator that
concentrations of this magnitude do
exist. The wide variability of the exposure
group sampling measurements
for worker 0152 indicate that dust for
the associated process is not being
controlled. Further, this variability reveals
that if this process continues
uncontrolled, even higher exposure
concentrations could occur. That is,
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