Biomedical Engineering Reference
In-Depth Information
Fig. 8.48 Acceptance limits for the LPM / SPM ratio that corresponded to grouped-stage accep-
tance limits for the established range of acceptable MMAD values; the red circles represent the
upper and. lower bounds for the ratio LPM / SPM
of original, left- and right-shifted data, 10,000 simulated APSD profiles were gener-
ated for a total of 30,000 profiles over a sufficiently wide range of MMAD values,
with characteristics similar to the original data and consistent with the mechanisms
involved in particle size shifts in OIPs.
This simulated data set was used to assess the performance characteristics of the
two approaches under a variety of comparable acceptance limits.
It was possible to compare the two approaches on the same basis under different
conditions, by using different combinations of distribution percentiles to set group-
ing acceptance limits (e.g., 5th and 95th versus 1st and 99th percentiles) as well as
different prediction intervals (e.g., 95% versus 99.9% prediction intervals). For
example, using the 1st and 99th percentiles to establish grouped-stage acceptance
combined with a 99.9% prediction interval to establish the MMAD range resulted in
48% and 0% false rejection (type I) and false acceptance (type II) rates, respec-
tively, for grouped-stage decisions based on combined group 2, 3, and 4 results.
A different scenario with the same grouping distribution percentiles but with a 90%
prediction interval resulted in a 0.09% type II error rate and a 21% type I error rate
for the grouped-stage approach. A variety of scenarios and the corresponding error
rates for the LPM / SPM ratio metric are shown in Table 8.9 .
It is also possible to apply a scaling factor to the prediction interval to adjust
acceptance limits for the LPM / SPM ratio to produce false acceptance rates to match
that of the grouped-stage method.
The results of these simulations can be presented in the form of OCCs. For exam-
ple, the scenario presented in the last row of Table 8.9 is shown in Figs. 8.49 , 8.50 ,
8.51 , and 8.52 .
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