Chemical Engineering July 2017 - 58

Out of specification (OOS) Results
Batch 1
Batch 2
Batch 3
Mean
Standard Deviation
Count
TABLE 4. PREDICTED OOS FREQUENCY FOR A SINGLE PRODUCT CHARACTERISTIC
Min & Max
59.7%
Six Sigma
10.7%
TABLE 5. VISCOSITY DATA & STATISTICS
394,000
341,000
418,000
384,333
39,400
3
similar to those of another product
that's been manufactured for a
while. Table 3 contains statistics for
the established product. Comparing
the proposed specification ranges
in Table 2 with information acquired
from the older product is informative.
Assuming both products have
identical viscosity-population distributions
allows one to estimate OOS
frequencies for the three specification
ranges (shown in Table 4). This
demonstrates how unsuitable the
first two methods can be at creating
specification ranges for situations involving
small data sets.
It should be noted that the OOS
percentages listed in Table 4 are for
a single quality parameter. If an invalid
methodology is used to create
the specification limits of more than
one quality parameter, the likelihood
of making OOS product increases
correspondingly. This is illustrated by
the two-factor probability equation
shown below:
P(A or B) = P(A) + P(B) - P(A and B)
If the odds of having OOS product by
parameter A are 10%, or by parameter
B are 10%, then the odds of having
OOS product from either A or B are
calculated using the following equation:
Desired release limits
3 Sets of test results
6 Sets of test results
2.7 - 3.3
LRL - URL
2.56 - 3.27
2.72 - 3.17
P(A or B) = P(A) + P(B) - P(A and B)=
(1/10)+(1/10) - [(1/10)*(1/10)] = 19%
Considering the negative consequences
typically associated with
manufacturing OOS products, they
should be avoided, especially when
they arise from routine variation, not
from a process deviation that could
adversely impact a product's quality.
Admittedly, small data sets sometimes
contain considerable variability.
Applying the Tolerance Interval
method to such data can lead to
very wide specification limits that are
neither feasible nor desirable. For instance,
the lower viscosity-release
limit could end up as a negative number,
which is physically impossible. In
all instances, before calculating a TI,
the following should be done:
Check for and exclude outliers/
anomalies from the data set. Several
statistical methods are available
for detecting outliers.
If the calculated TI is still wider
than expected or desired, proceed
with one of the following options:
Option
1.
Propose a narrower,
more pragmatic specification range
and identify what confidence level
corresponds with it. The confidence
level associated with a tighter, but
more reasonable, specification range
can be computed. If the confidence
TABLE 7. EFFECT OF UTILIZING ADDITIONAL DATA POINTS ON TOLERANCE INTERVALS
Drug active #1
Drug active #2
6.75 - 8.25
LRL - URL
6.05 - 8.99
6.79 - 8.16
Drug active #3
0.45 - 0.55
LRL - URL
0.43 - 0.58
0.47 - 0.53
FIGURE 1. Shown here is
the predicted population distribution
for the calculating
confidence level example
100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000
56
To determine 1- one should specify
the degrees of freedom (N-1) and calculate
the Chi-square cumulative distribution
function (Some spreadsheet
programs or online calculators can do
this computation). The result is 0.332.
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JULY 2017
Tolerance Interval
0.0%
TABLE 6. PROPOSED VISCOSITY RANGES
Tolerance
interval
23,306
Alternative
range
Lower release
limit (LRL)
Upper release
limit (URL)
745,361
200,000
500,000
level turns out to be sufficiently high,
the adjusted specification range
should be adopted. An example of
how to do this is discussed below.
Option 2. Generate some supplementary
preproduction data. Producing
just a few additional test
results (not the 30-50 data points
required by other specification setting
techniques) ordinarily leads to
enough convergence between observations
so that the Tolerance Interval
will shrink considerably. The
k2 value is driven down through increased
knowledge about the new
product, and the standard deviation
generally decreases as well. This is
demonstrated in an example below.
Calculating confidence level
Discussed next are recommendations
for calculating the confidence
level of a designated specificaiton
range. Table 5 shows viscosity data
associated with a very thick product.
Since these data were not consistent,
the proposed viscosity range
using Tolerance Intervals, as shown
in the middle column of Table 6, was
quite wide. The LRL (at a 90% confidence
level) was unacceptably low
at only 23,306 cps. As a result, an alternative
viscosity range of 200,000-
500,000 cps was proposed and
evaluated. What confidence level
coincides with that range when 99%
of future production viscosities must
fall within that range?
Referring to Figure 1, since the
average viscosity of 384,333 is not
the midpoint of the proposed range
of 200,000 - 500,000, both sides of
the population distribution will be examined
separately. For the lower tail
of the distribution:
LRL=
kL =
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Chemical Engineering July 2017

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