The following metrics were used to characterize the homogeneity of
the blends:
1) The maximum difference (MD) in the average potency of API X
among samples taken from multiple locations of the powder bed
from the same process step, which is shown in Eq. (1)
MD ¼ Max Xi
−Min Xi
ð1Þ
where Xi is the average potency at a specific location i. If samples are
taken only from the top and bottom of the bin blender (68 L),
MD ¼ XT−XB
ð2Þ
where XT and XB stand for the average potency of the sample from
the top and bottom of the bin blender, respectively. MD indicates
the macro-mixing behavior and is expected to be close to zero for
effective macro-mixing.
2) The relative standard deviation of potency measurements within a
sample, or RSDS, as is shown in Eq. (3),
RSDS ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Xn
j¼1
Xi j−Xi
2
n−1
Xi
vuuuuuut ð3Þ
where n is the number of potency measurements within a sample, Xij
is an individual observation of potency at a specific location i. RSDS is
an indicator of micro-mixing behavior at a specific location with a
low RSDS suggesting a uniform distribution of API X in the vicinity of
that sampling location.
3) The relative standard deviation for potency measurements from all
samples within a particular mixing step, or RSDm, which is shown in
Eq. (4),
RSDm ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
i¼1
k Xn
j¼1
Xi j−Xm
2
N−1
vuuuut
Xm
ð4Þ
where k is the number of sampling locations, N is the total number of
potency measurements across all samples from a particular mixing
step (N=k ∗ n), and Xm is the observed mean of all these individual
measurements in the mixing step. RSDm represents the overall mixing
behavior of a specific mixing step. A powder mixture that is well
mixed at the micro- and macro-scales yields a low RSDm value while
1st bin
Blend 1
Top Sample
Bottom Sample
2nd bin
Blend 2
Top Sample
Bottom Sample
Comil
2nd bin
Blend 3
Top Sample
Bottom Sample