Biomedical Engineering Reference
In-Depth Information
Christopher, et al. [
8
]). Note that the fitted parameters in this model directly
relate to the
MMAD
value, maximum size limit, minimum size limit, and
“steepness” of the cumulative mass-weighted form of the APSD. Besides
MMAD
and steepness, the parameters include the two asymptotes (i.e., the minimum and
maximum mass), noting that the former is forced to zero.
4. Define two cumulative particle size distributions that bracket the reference/ideal
cumulative APSD fit in step 3. These two cumulative particle size distributions
represent distributions that are considered equivalent/similar to the reference/
ideal. The degree of sameness/similarity to the reference/ideal APSD was estab-
lished by computing a goodness-of-fit statistic between the displaced cumulative
APSD and the reference/ideal APSD. That procedure is described below. Region
of similarity to the target APSD moving the distribution below and above—self-
imposed similarity—reproducible methodology for characterizing minimum
and maximum batches with similar APSD properties and
MMAD
value.
5. From the displaced cumulative APSD distributions, limits that represent equiva-
lency to the reference/ideal APSD curve could be calculated for
MMAD
,
LPM
/
SPM
ratio, and grouped stages. This procedure
1
established “goalposts”
across all three metrics of equivalency to the reference/ideal cumulative APSD
metric. Label these equivalency “goalposts”
θ
L
and
θ
H
.
6. Based on the parameter estimates from step 3, create a series of cumulative
APSDs where only the
MMAD
was varied.
7. Compute the corresponding APSD metrics (
LPM
/
SPM
ratio and grouped stages)
from the series of cumulative APSDs generated in step 6.
8. Assuming standard deviations for
LPM
/
SPM
of ±0.05 and ±1% LC for each
stage grouping and an acceptance criterion based on a single measurement, cal-
culate the probability of meeting the limits established; i.e., calculate the follow-
ing probability:
q
££
æ
ö
÷
»
prob
()
q
X
H
normal
(, .
ms
=
005
or
s
=
1
%)
(8.4)
ç
L
X
where
X
represents either
LPM
/
SPM
ratio or grouped stages and
μ
represents the
appropriate metric value computed in step 7 from the series of cumulative APSDs
that generated varying
MMAD
. The observed data, either ratio or grouped stages,
were unimodal and approximately symmetric; therefore, normality is not an
unreasonable approximation from which to base the comparison.
9. The final OCCs are a plot of probability acceptance or probability of the appro-
priate metric producing values within the equivalency goalposts, plotted as a
function of
MMAD
.
1
It should be noted that the assumed limits were established by computing a goodness-of-fit
statistic between each displaced cumulative APSD and the target cumulative APSD. Several levels
of this statistic (0.9, 0.8, 0.7, and 0.6) were applied to each studied product, and the resulting limits
are provided in Table
8.6
. While this provided a systematic process for establishing assumed lim-
its, the actual values are not critical. The important constraint for comparing the performance of
the two metrics is that each particular limit was converted to equivalent requirements with respect
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