Solutia
Richard W. Miller (850) 968-8358 Fax: (850) 968-8732
From:
“Solutia Fellow” [rwmill@solutia.com]
September 24, 2008
Date:
Analysis of the 41LDC Manufacturing Process and the AEG Measurement System with an
Subject:
Emphasis on Resampling Out-of-Spec Lots
Summary
Greenwood’s (GWD) AEG measurement system, validated utilizing the 5/3 strategy (five
routine samples split into thirds with their variance estimates pooled), accounted for ~12% of
41LDC’s total AEG variation. While this process was judged capable (Ppk=0.99), the long-term
component of variation was significantly greater than its short-term component. Finally, the routine
re-measure of out-of-spec material is a good strategy when the measurement system variation
component is small enough; otherwise, the β risk (customer risk of accepting out-of-spec material)
increases dramatically.
Jeff Wang, Gordon Mayfield and I are in the process of setting up continuous measurement
system validation for important polymer characteristics (AEG, RV, TiO2, H2O) at Greenwood.
This report summarizes the AEG characterization of 41LDC made on CP 45 between 6/11 &
8/19/08. In addition to summarizing the process data, a probabilistic argument for resampling out-
of-spec material is presented.
Major Observations & Recommendations
• AEG measurement system accounted for ~12% of GWD’d 41LDC (CP 45) variability;
• While GWD’s 41LDC manufacturing process is capable (Ppk=0.99 for in process
sampling), its capability could be improved significantly (Ppk=1.34) by reducing long-term
variation: campaign-to-campaign centering and variation fluctuation, and general process
drift;
• Initiate measurement system validation (GWD and Pensacola(PNS)) for other important
product properties (e.g., RV, TiO2 and H2O for 41LDC);
• Assess risks of out-of-spec sample re-measure through estimation of each measurement
system’s sigma; a sample measuring USL+1σ Meas Sys or greater than LSL - 1σ Meas Sys
will have a 16% chance of falling within specs on re-measure (even without analytical
error), a 32% chance on two re-measures, a 48% chance on three re-measures;
• Not all in-spec measurement distributions are equal; the level of variation can be more
important than the targeting because customer satisfaction is maximized at the minimum
2 2
in the Taguchi Loss Function {min(TLF) = min (σLT + (Target – μ) };
• When a customer identifies a spec range as USL – LSL, that means the producer’s
effective spec range must be redefined tighter as USLeff=USL-xσ Meas Sys and
LSLeff=LSL+xσ Meas Sys where x might vary between 0 and 6 depending on the level of
customer risk (calling out-of-spec product good) desired.

Greenwood’s 41LDC AEG Process Capability
Chart 1 plots single AEG measures made over this two-month production period. While
this is in-process data—data used to control the CP line—the pack-out (P/O) characteristics were
similar. Red lines mark the population mean and upper and lower control limits (μ +/- 3σST), while
the blue lines mark specification limits (45 +/- 1.2). The first represents the “voice of the process”;
the second restrictions imposed on the process—ideally by customer needs. One can expect
99.73% of the population to fall between the outside red lines when there’s no long-term
component of variation (process drift or campaign-to-campaign centering). When a point falls
beyond the red lines, it’s deemed a special cause, i.e., likely to come from a different population
because of some special cause.
Often, the special cause for an outlier data can be tracked down and changes made to re-
center a shifted process, but just as often the reasons for the shift go unresolved and
compensatory adjustments are made anyway. The BCF process is a good example of the latter
where temperature adjustments are routinely made to re-center positions that continually drift as
process components age and foul.
There’s also the very real possibility of a questionable measurement, either because of
outright error or because of the distributional nature of the measurement system itself. Because
this producer risk (risk of off-grading acceptable product) is often judged more important to the
producer than customer risk (risk of not off-grading unacceptable product), off grade material is
given every opportunity to prove itself before being committed to a rework strategy. The question
then becomes: If the same lot is re-measured how likely is the new measure to fall within specs?

If a point falls beyond the specification limits (beyond the blue lines), especially for P/O data, it’s
common practice to re-measure that lot before reworking it to meet specifications. I’ll address the
resample question and its risk more fully in a later section.
This process’ capability matrix is shown in Chart 2. Specification limits, population mean
and its two measures of variation (short-term sigma and long-term sigma) are used to calculate
the capability metrics (Ppk, Pp, Cpk, Cp and % out-of-spec material) as defined in the chart. The
first column houses capability estimates for the current process, while the other three columns
calculate these metrics for other choices of specification limits. Note, the basic difference
between the two product capability metrics (Ppk and Pp) and the two process capability metrics
(Cpk and Cp) lies in the nature of their respective variation components: the first uses long-term
sigma and characterizes the product the customer receives, while the second uses short-term
sigma and characterizes the ultimate capability of the process.
These metrics confirm Chart 1’s picture: GWD’s 41LDC process is pretty capable (Ppk
nearly 1.0) with blue specification lines well outside the red control ones. The difference between
Ppk and Pp (and Cpk and Cp) indicates a slight centering problem, while the difference between
Ppk and Cpk indicates a significant long-term variation component. If this process could be re-
centered and its long-term component of variation reduced, it’s capable of producing a 1.49 Ppk
(making virtually nothing out-of-spec), i.e., spec range / 6σ = 1.49 means the spec range would
contain ~9 σLTs. Note, a Ppk=1 means the spec range would contain 6 σLTs.

5/3 Strategy: AEG Measurement System Validation
The following table summaries AEG data collected from the 5/3 testing where five routine
samples were split into thirds then characterized blindly on three different shifts. The idea is to
get routine measurement system data which reflect true lab variation. Assuming the subsample
compositions are identical (a good blend), their pooled variance estimate provides our estimate of
2
the measurement system’s variance. Here, σ is estimated to be 0.016 for the AEG
Meas Sys
2
measure, which in turn, accounts for ~12% of the total variation (σ LT) evident in the Chart 1 data.
Note, the 5/3 strategy follows this initial 2-week sampling with another single sample split
every two weeks. Continuous validation of the AEG measurement system is thus provided at the
cost of a single extra sample each week.

Chart 1 from a Probabilistic View and the Resampling Question
The data presented in Chart 1 can also be looked at through the prism of probabilistic
models, which then enable us to ask questions: How does the difference between short-term and
long-term variance impact the frequency of control limit (μ+/-3σST) and specification limit
violations? How does a process shift impact quality? What is the impact of resampling a lot after
it has experienced an out-of-spec signal the first time? And finally, how does measurement
system variation influence the risk of resampling? Note, this modeling assumes the data are
normally distributed—a good assumption for these data.
The black distribution shown in Chart 3 depicts the probability distribution represented in
the AEG data plotted sequentially in Chart 1 (inset in Chart 3 as well). It describes the frequency
of AEG measures as a function of AEG level. The red distribution is that black distribution
hypothetically shifted to the high side by two long-term standard deviations, and the blue
distribution is the measurement system’s distribution expected for a lot which has measured an
out-of-spec 46.5 AEG in its routine sampling. The green vertical lines mark the process’ target
and specification limits, while the blue vertical lines mark control limits for the black distribution.
Note, the black distribution, called process State A is slightly off center to the high side of target
(hence the Ppk-Pp capability differences).

Chart 4 shows the percentage of each of the above distribution’s population that lies either
below or above the specification, control and target limits. A further distribution, the measurement
system centered at the upper specification limit, is included as well. Several points become
clearer.
First, short-term sigma are used in Shewhart charts to define control limits (μ +/- 3σST)
where the sigma are calculated for single-point measures from a 2-point moving range and for
multi-point averages from their within sample group variances. The State A distribution, on the
other hand, reflects the long-term sigma variation. It’s the variation one gets by throwing all 174
data in Chart 1 into a hat and calculating its variance. The net effect, since 3σST <= 3σLT, is that
the routine data can be expected to violate its μ+3σST limits more frequently than expected. For
example here, State A violates the lower control limit (LCL) at a 1.40% frequency (1 in 71 data)
and the upper control limit (UCL) at a 1.38% frequency (1 in 72 data); whereas a typical Shewhart
chart is cited to violate either control limit at a 0.135% frequency (1 in 740 data). Obviously, the
producer’s risk (calling good product bad) increases appreciably when σLT >>> σST.
The second question asks how a process shift (the red distribution, a +2 σLT, in Chart 3)
impacts quality. First, is there really any difference between two lots measuring a 46.75 AEG
where the first one comes from un-shifted (black) distribution and the second from the shifted
(red) distribution? No, as far as we can measure, the two are identical. What’s different is the
shifted distribution can be expected to produce 17.09% of its lots above the upper spec limit,

while the original distribution can be expected to place only 0.16% there. That’s why one should
be concerned about a shifted process. Note too, the shifted process is far more likely to produce
a runs-rule signal, e.g., the next 8 points in the black distribution would be expected to fall on one
side of its mean 0.39% of the time {(0.5)^8} or 1 time in 256 groups; whereas, the shifted red
distribution would be expected to signal that 8-point grouping to the high side of the original (black
distribution) mean 83.2% of the time.
The final two questions focus on the measurement system. Now that we can estimate the
measurement system’s variance, we can better assess both the risk of a re-measure and our true
spec limits. Remember, we re-measure a given lot of the red or black distribution in Chart 3;
whereas both of these distributions reflect the breadth of their respective lot measurements. The
blue distribution in Chart 3 outlines the frequency of AEG measures that one could expect from
just taking the original sample (AEG=46.5) and re-measuring it a number of times. Note, 46.5 is
2.4σMeas Sys above the 45.93 USL. We’re assuming there’s no difference in the sample, just this
level of variation in the measurement system itself (similar to the assumption made in the 5/3
sampling strategy). In the particular measurement distribution shown, virtually 99.18% of the
distribution lies above the 46.2 USL so any re-measure is likely to remain out-of-spec. Of course,
that assumes that no error occurred in the original measure. That means if the re-measure falls
within spec limits, there’s likely been an error made in the original measure.
Let’s look at another sample. Say we measure AEG for a lot at 46.2, exactly on the USL
and decide to resample. Given the variation in the measurement system, a single re-measure will
produce an out-of-spec signal 50% of the time and an in-spec signal 50% of the time. Moreover,
if I were to resample two times, there would be a 75% chance of getting an in-spec signal, three
times a 87.5% chance. In this case, producer’s risk (calling good product bad) has been judged
far more important than customer’s risk (calling bad product good). So now let’s reformulate spec
limits to reflect the measurement system’s variation.
Assume that customer’s risk is most important to us. To ensure that no product leaves the
building outside spec limits, one needs to use effective spec limits: USLeff = USL - 3σMeas Sys, here
45.83 (46.2 – 3x0.125) and LSLeff = LSL + 6σMeas Sys or 44.18 (43.8+3x0.125). Obviously,
managing variation is critical to quality.

Variation and Customer Preferences
Traditionally, quality has been viewed as a step function where product is judged either
good or bad depending on whether it falls within specification limits or not. Taguchi put forth the
idea that the customer becomes increasingly dissatisfied as a product drifts from target, even if
that product stays within spec limits. The customer desires a product that is constant part-to-part,
lot-to-lot or bobbin-to-bobbin. The producer, on the other hand, desires to make and sell as much
2
A-grade material as possible. Each lot contributes to the (Target – μlot) , while their aggregate
2
variation determines the σLT term.
2 2
Customer Satisfaction: Taguchi Loss Function {min(TLF) = min (σLT + (Target – μlot) }
Clearly, in some cases—like the two distributions in the chart below—variance (even with in-spec
material) is more important to customer satisfaction than targeting.
The following chart further demonstrates the point. In these two distributions is there really
any difference among lots A, B and C? Don’t all differ significantly from lot D? Which of the two
distributions do you think will produce more consistent product for the customer? The answers
are obvious: the right-side distribution, though it has a targeting problem, would both be easier to
use by the customer and easier to control by the producer. The left-side distribution has a
variation problem. Even though everything falls inside spec limits, it will be harder to use by the
customer.
This is essentially the problem that the low-melt yarn program has run into over the past
few years. EMS produces a low melt resin that met melt viscosity specs, though their lot-to-lot
variation looked much like the left-side distribution below. The problem came when we (the
customer) tried to spin their resin: those lots from the high-side of the distribution required far

different (sometimes unknown) process settings than those lots from the low-side of the
distribution required. As a consequence, much of the yarn ends up on the floor as the process re-
equilibrates, and yields suffered. Again, the message is clear: variation is critical to quality.