From Figure 5, the simulated tolerance interval is from 82.7 (0.5% quantile) to 94.4 (99.5% quantile). Note that the interval
is slightly wider and shifted to the left from the interval computed using equation (1). The increased width is due to the
propagation of error caused by the movement in OP2 and OP3, and the shift to the left is due to OP3 being centered to the
left of its setpoint (45).
Note the distribution of the PP in Figure 5 is centered at 88.6 instead of at the desired large-scale GMP mean of 89.5. Recalling
that the spread of a tolerance interval is not affected by shifts in location, the interval is adjusted to the desired GMP
center by taking as the lower bound 82.7 – (88.6 – 89.5) = 83.6 and as the upper bound 94.4 – (88.6 – 89.5) = 95.3.
Figure 7 presents actual PP values from the validation runs for which these criteria were established. The difference between
the intervals for Scenarios 2 and 3 in Figure 7 is not great because there is not a particularly strong relationship between
the PP and the OPs in this example. (R-square in Table 3 is only 0.241). There will be a greater disparity between these two
sets of limits when the strength of the linear relationship between the PP and OPs is greater. However, note that by making
use of bench data and regression analysis, intervals from scenarios 2 and 3 are much shorter and more representative of the
values obtained in the validation runs than the limits computed with only the large-scale GMP data.
The procedure described in this paper is general enough to apply to more complex situations. In particular, it is often the
case that random events such as differences in column feed material will increase the variability in a PP. The regression
model can be modified to appropriately incorporate random effects, and the JMP simulator used to produce a tolerance interval
under these conditions. Quadratic effects and interaction effects among the OPs are also easily incorporated into the regression
In conclusion, we have presented approaches that yield appropriate VAC. The most appropriate technique for establishing these
ranges depends on the available data. For many processes, movement by an OP within the OR is expected. Combining bench-and
large-scale data sets, analyzed using the simulation approach presented in this paper, results in VAC that are indicative
of process control, yet are not unnecessarily restrictive.
Rick Burdick is a principal quality engineer in the Quality Engineering and Improvement department at Amgen; Tom Gleason is a senior associate scientist in the Manufacturing Science and Technology department at Amgen 303.041.1432, firstname.lastname@example.org
Steve Rausch is a senior scientist in the Manufacturing Science and Technology department at Amgen; and Jim Seely is a director in the Manufacturing Science and Technology department at Amgen.
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