Theory of Constraints

MULTIVARIATE MODELLING, FAULT DETECTION, AND VALIDATION FOR THE EXTRUSION PROCESS D.O. Kazmer1, S. Johnston1, L. Abou-Shady1, D. Hazen2, and C. Ambrozic2 1

Plastics Engineering Department, University of Massachusetts Lowell 2 MKS Instruments, Andover, Massachusetts Abstract

An auxiliary process monitoring system was implemented for an instrumented tubing extrusion process. The system incorporated multivariate modeling in the form of Principal Components Analysis (PCA) and Projection to Latent Structures (PLS). A design of experiments was performed to train four PCA and four PLS models using different sets of input and output variables. Validation experiments were subsequently performed to evaluate the models capability to detect 18 imposed process faults. Results indicate that Shewhart control charts of process variance and model residual errors are well suited for detecting faults in the extrusion process.

Introduction Extrusion is a process in which a viscous polymer melt is forced through an opening in a die to form an extrudate having a constant cross-section. Dimensional tolerances in extruded products are typically quite wide since the extrudate cools in an unconstrained manner from a high bulk temperature; the quality of the extrudate is sensitive to variations in material properties and process states. As such, statistical process control is widely relied upon. Rauwendaal [1] suggests that there are typically ten important process parameters which should be monitored in extrusion, which are critical to quality. These parameters may include extrudate dimensions, die head pressure after screen pack, barrel pressure before screen pack, polymer melt temperature, motor load, screw speed, take-up speed, power consumption of heating zones, cooling rate of cooling zones, barrel and die temperatures. Multivariate analyses have been utilized in the injection molding process for process monitoring and for fault detection [2-4]. This paper extends the use of multivariate analyses to the extrusion process. Relative to other research in multivariate quality control of extrusion [5-7], the goal of this work is 1) to validate the effectiveness of PLS and PCA models in identifying common process faults in an extrusion process through the use of Shewhart style process control charts [8], and 2) to provide practical guidance on extrusion instrumentation suites and quality control techniques.

Multivariate Modeling At discrete times, the output measurements from the extrusion process, Y, can vary significantly from the machine set-points, U. There are two reasons for this. First, the process outputs may lag or otherwise

stochastically vary from its governing machine set-point. For example, a thermocouple providing temperature feedback to a barrel heater may lag due to the thermal mass of the barrel or oscillate due to the cycling of the heater. Second, there are many process outputs (such as melt pressure, screw torque, and melt viscosity) that do not have a direct mapping to any single machine setting. Such process outputs are commonly measured and often used as the final indicators of manufactured product quality, yet are governed by multiple machine settings. Principal Component Analysis (PCA) is used to provide statistical measures of process performance since a well instrumented process can literally provide hundreds of data points for each manufacturing cycle. Maintaining all of the input data, X, is redundant since it is highly inter-related. As such, PCA reduces the redundancy by introducing new variables or principle components, P, that consists of orthogonal linear combinations of the original variables: 𝐗 = 𝐓𝐏 ′ + 𝐄 (1) where T are the scores and E are the residuals. The resulting model will typically have far fewer principle components than the original number of process states while explaining more of the observed process variation than a conventional linear regression. The PCA provides two statistics of the process behavior: the Hotelling t2 and the residuals’ standard deviation or DModX [9]. The Hotelling t2 value is: 𝑡 2 = 𝑛(𝑥̅ − )′𝐖 −1 (𝑥̅ − ) (2) where 𝑥̅ is the mean for a sample x,  is the global mean, and W is the sample covariance. As such, the Hotelling t2 value represents the distance of a sampled observation from the center of the PCA model. The DModX is defined as the normalized residuals: DModX = 𝒆 ∙ 𝒆′⁄(𝑀 − 𝐴) (3) where M is the number of columns in X and A is the number of principal components. The vector of residual errors, e, is defined as: 𝒆 = 𝒙 − 𝒕𝐏′ (4) The DModX value is the residual standard deviation calculated from the residuals, i.e., after subtracting the accepted model behavior from the scaled and centered process data. A high DModX score indicates that the current process observation is deviating from the expected behavior of the model and so can be considered as a measure of the uncertainty while the t2 statistic can be considered a measure of the variation.

SenselinkTM Implementation: Tubing Extrusion Line

Davis Standard Single Screw Extruder (6 signals)

SenselinkTM

Puller (1 signal)

Water Bath (1 signal) Optical Micrometer (2 signals)

Tubing Die (2 signals)

Not Shown: 1) Temperature Controller for Water Bath 2) Micro Air Pressure Regulator (1 signal)

Figure 1: Single screw tubing extrusion line

Instrumentation A single screw extruder that fed a cross-head tubing die was used for this experimentation. The extruder was a Davis Standard extruder (Model: DS-10HM, Serial # 58827) having a 25 mm diameter screw. By changing the process conditions, the extrudate dimensions could be varied between 0.108 to 1.472 mm for the inner diameter and between 0.772 to 2.075 mm for outer diameter. A 70/30 blend of LDPE (Exxon Mobil, Grade: LD 105.30) and LLDPE (Dow, Engage 8842) was the base resin. The extrusion line was instrumented as shown in Figure 1. Six J-type thermocouples were used to measure the temperatures of the feeding zone, metering zone, die, die clamp, water bath, and melt temperature at the screw tip. Pressure transducers were used to measure both the melt pressure at the tip of the screw and tubing air pressure at the pressure regulator exit. The screw speed and motor load were acquired from the machine’s motor controller while the puller speed was acquired from the extrudate puller’s motor controller. In addition, the vertical and horizontal diameters of the extrudate were acquired from an optical micrometer (Target Systems Inc. model XY4010). All signals were connected to an auxiliary process controller (MKS SenseLinkTM) that sampled data at 10 ms intervals.

Experimentation A design of experiments (DOE) was performed to characterize the process behavior with respect to nine different factors including: barrel temperature, screw rotation speed, line puller speed, polymer blend ratio, die temperature, water bath temperature, water bath flow rate, tubing internal air pressure, and extrudate free length between the die lip and the water bath. Table 1 lists the factors, their observed standard deviations at steady state, and the minimum/maximum values applied during the training DOE. The range was selected to ensure a high signal:noise ratio relative to the normal process variation.

Table 1: Extruder DOE factors and their statistics

Factor Min Center Max Std Dev

Barrel Screw Puller Poly Die Water Flow Temp Speed Speed Blend Temp Temp Rate (C) (RPM) (cm/s) (%) (C) (C) (cc/s) 1 2 3 4 5 6 7 197 15 9.8 60 197 40 64.1 199 20 10.0 70 199 43 78.3 201 25 10.3 80 201 46 91.3 0.28 1.20 0.02 1.00 0.28 0.28 1.85

Air Free Pres Length (bar) (cm) 8 9 60.8 1.91 67.6 2.54 74.4 3.18 0.68 0.13

Table 2: Fractional Factorial Design of Experiments Barrel Screw Puller Poly Die Water Flow Air Free Run Temp Speed Speed Blend Temp Temp Rate Pres Length Column 1 2 3 4 5 6 7 8 9 Factor 1 2 3 4 1*2*3*4 1*2*3 1*3*4 2*3*4 1*2*4 0 0 0 0 0 0 0 0 0 0 1 -1 -1 -1 -1 1 -1 -1 -1 -1 2 -1 -1 -1 1 -1 -1 1 1 1 3 -1 -1 1 -1 -1 1 1 1 -1 4 -1 -1 1 1 1 1 -1 -1 1 5 -1 1 -1 -1 -1 1 -1 1 1 6 -1 1 -1 1 1 1 1 -1 -1 7 -1 1 1 -1 1 -1 1 -1 1 8 -1 1 1 1 -1 -1 -1 1 -1 9 1 -1 -1 -1 -1 1 1 -1 1 10 1 -1 -1 1 1 1 -1 1 -1 11 1 -1 1 -1 1 -1 -1 1 1 12 1 -1 1 1 -1 -1 1 -1 -1 13 1 1 -1 -1 1 -1 1 1 -1 14 1 1 -1 1 -1 -1 -1 -1 1 15 1 1 1 -1 -1 1 -1 -1 -1 16 1 1 1 1 1 1 1 1 1 17 0 0 0 0 0 0 0 0 0

Table 2 provides the normalized DOE settings for each run where the -1, 0, and 1 values respectively represent the minimum, center, and maximum values for each factor listed in Table 1. The training DOE is a fractional factorial design, 29-5, augmented with center point runs at the start and end to verify model linearity and process consistency. The factors and their ranges were selected to capture a broad range of variation that

Table 3: Literal and virtual process states Literal Process States Virtual Process States Zone 1 & Zone 3 Temperatures Mass flow rate (Q) = v * D^2 Die 1 & Die 2 Temperatures Torque (Tq) Melt Temperature (Tm) Viscosity 1 = P / Q Melt Pressure (P) Viscosity 2 = L / RPM^2 Screw Speed (RPM) Consist. Index = Q / RPM^(1+n) Motor Load (L) Draw Ratio = v / Q Water Bath Temperature Specific Mech. Energy = RPM * Tq / Q Tubing Internal Air Pressure 1/Melt Temperature Diameter 1 & 2 of Tube (D) 1/Pressure = 1/P Puller Speed (v) 1/RPM

Table 4: Different types of models developed Model PCA1 PCA2

Data Just machine sensors Machine sensors, on-line laser micrometer, and virtual process states On-line laser micrometer signals modeled as a function of machine sensors, and virtual process states Off-line tubing dimensions and tensile strength modeled as a function of the machine sensors, on-line laser micrometer signals, and virtual process states

PLS1 PLS2

Table 5: Correlations of each model type Zone 1 Temperature Included? Yes No 0.661 0.73 PCA1 (3 PCs) (3 PCs) 0.724 0.754 PCA2 (4 PCs) (4 PCs) 0.604 0.631 PLS1 (3 PCs) (3 PCs) 0.697 0.74 PLS2 (5 PCs) blind_tubing.M2 (PCA-X), PCA (5 & PCs) no min/max, PS-Complement Model 10 XVarPS(Avg Zone1 Temp) Model

184 363

XVarPS(Avg Zone1 Temp)

might be observed during one or more very long production runs. For each run, the extruder was allowed to equilibrate for thirty minutes after which sixteen minutes of process data and extrudate were collected. The data obtained from the training DOE was statistically analyzed to provide minimum, maximum, and average values for each sensed data stream every 10 seconds. These literal process states were augmented with “virtual” process states that were calculated by combining one or more literal states. Prior work in on-line process modeling of injection molding suggests that there are certain process states and other transforms of process data that may prove excellent determinants of the underlying process response [10]. The addition of such virtual process states provides on-line estimation of real polymer states that are not directly observable, but likely have a significant impact on the quality of the manufactured product. Table 3 details the literal and virtual process data that were defined for the extrusion process. In addition to the online metrology, samples of extrudate were collected for each run in the training DOE. The tubing was sectioned at five equidistant locations across the length of the manufactured extrudate, measured using an optical comparator, and tensile strengths tested. Four different types of models were developed as listed in Table 4. The simplest model, PCA1, is a principal components model that considers only the process states originating from the extruder’s sensors; this dataset is quite typical of conventional extrusion set-ups. The second model, PCA2, is a principal components model that considers the extruder signals, the horizontal and vertical diameters from an on-line laser micrometer, and the virtual process states defined in Table 3. For greater predictive capability of the extrudate quality, PLS1 is a Projection to Latent Structures that models the laser micrometer output signals as a function of the literal and virtual process states from the machine sensors. Finally, the most sophisticated model is PLS2, which is a Projection to Latent Structures that models the off-line metrology of the tubing dimensions and tensile strength as a function of the machine sensors, on-line laser micrometer signals, and virtual process states. The models described in Table 4 are listed in order of increasing information content, and the hypothesis to be tested herein is that the fidelity and predictive capability of these models are likewise increasing. During the model fitting, it was observed that the sensor stream associated with the zone 1 temperature exhibited a high degree of noise. This behavior is plotted in Figure 2 across 8200 observations, in which the average zone 1 barrel temperature was 183 C and the range of the noise was approximately 1 C. Since this zone temperature was not changed except for one induced fault near observation 3500, the inclusion of this signal could adversely affect the model fidelity. To investigate the issue of including a signal with a low signal:noise ratio, a second set of four models was developed that did not include the zone 1 temperature signal. Table 5 plots the correlation coefficient for the two sets of four models.

362 183

361 182

360 181

359

180

358 0

1000

2000

3000

4000

5000

6000

7000

8000

Observation Num Number 11 - 10/13/2011 7:10:53 AM FigureSIMCA-P+ 2: Zone 1 temperature

It is observed in Table 5 that the number of principal components (PCs) in each of the four types of models varies. During model fitting, the number of principal components is automatically selected to maximize the information content per additional principal component. In general, a greater number of principal components is indicative of higher model complexity and should be able

to explain a greater proportion of the process behavior than models with a lesser number of principal components. It is observed that those models providing Projection to Latent Structures, PLS1 and PL2, have a lower correlation coefficient than the PCA models. The cause is that these models provide input:output relations between the input signals and the quality metrics. Noise in the quality metrics and/or non-linear relations between these metrics and the input signals will tend to reduce the correlation coefficients relative to PCA models. In Table 5, it is observed that the number of principal components for each type of model is the same regardless of whether or not the zone 1 temperature signal is included in the model. This consistency is an indicator that the zone 1 temperature signal is not a significant driver of the model behavior; its inclusion does not warrant the addition of a principal component with a heavy dependence on zone 1 temperature. Interestingly, the exclusion of zone 1 temperature does provide a consistent increase in the model correlation coefficient. This increased correlation is due to the reduction in random variation associated with the input signals, which forms the denominator in the calculation of the correlation coefficient. The predictive capability of the various models will be later analyzed by blind validation. To confirm the consistency of the multivariate models, the loadings biplot for each of the eight models are provided in Figure 3. Each of the eight plots provides the relative correlation between the included process signals. For example, the upper left plot, corresponding to the PCA1 model with zone 1 temperatures, indicated that the zone 1 temperature, puller speed, and water bath temperature are located near the origin and so have low importance. There are two other clusters of signals, with the top grouping including the zone 3 temperature, melt temperature, and die temperature. By being grouped together, these variables tend to have similar process effects and are different than the motor torque, screw speed, and air pressure that are grouped at right. The right top graph is for the PCA1 model without zone 1 temperature. It is observed that the exclusion of the zone 1 temperature has a negligible effect on the principal components. By comparison, the bottom left graph corresponds to the PLS2 model in which the off-line metrology of the extrudate is modeled as a function of the literal and virtual process signals. This model includes many signals, and it is observed that the model suggests that the die pressure and screw speed are highly correlated, and loosely correlated with the specific mechanical energy (SME). This finding is well supported by polymer processing theory. The model outputs are shown in red and include the modulus (E1), maximum stress (S_max), inner diameter (ID), and others. The model again correctly indicates that these outputs are related to the draw ratio. Other process correlations can be gleamed from the

biplot. Comparison of the bottom-left and bottom-right plots indicates that the zone 1 temperature does not have a significant influence on the model behavior. As may be expected, the PCA2 models are quite similar to the PCA1 models, as are the models for PLS1 and PLS2. In each case, the addition of new signals does not greatly alter the relative influence of the previously included signals. It is noted that there are substantial differences between the PCA and PLS models, driven by the different objective of the PLS model to provide predictive capability of the quality metrics. Moreover, the inclusion or removal of zone 1 temperatures does not significantly alter the behavior of the models.

Blind Validation A set of validation experiments were performed to determine the capability of the models to detect 18 randomly imposed process faults. The center point conditions from the training DOE, run 0 and run 17, were used as the nominal process for the blind validation. After the process had stabilized, data were collected at the center point conditions for 30 minutes. Following this the first fault was induced and data was collected for the run. At the start of each subsequent run any previous faults were reset and a new fault could be introduced. Each run was 30 minutes long with center point runs randomly distributed throughout the fault runs rather than being run after each fault. The effect of prior faults would diminish during a run while the effect of the new fault would stabilize during the run. An effort was made to choose faults that would affect all portions of the extrusion process, have different magnitudes, and that were both observable and unobservable by the process sensors. All data was collected without record of the faults and the process was analyzed using each of the models described above. The PCA and PLS models track the process variation by a score of the distance to the model (DModX) as well as the process behavior by the Hotelling t-squared (t2) value. These two measures form the basis of the Shewhart-style control charts provided in Figure 4. Specifically, each set of graphs provides the corresponding model’s DModX and t2 values for the validation experiments, in which each observation corresponds to the average statistics across a 10 s time duration. The horizontal lines indicate the control limits generated for each model at a 95% level of confidence. According to statistical process control methods, the control system will trigger an alarm when either of these measures is outside the outer limit, consistently outside the inner limit, trending towards a limit, oscillating in a systematic manner, and for other reasons. In Figure 4, the vertical shaded bars are intended to facilitate identification of the various validation runs listed in Table 6. All eight models were able to correctly identify the center runs numbered 18, 29, 31, 35, and 38 as within control.

Model

With Zone 1 Temperature

Without Zone 1 Temperature

PCA1

PCA2

PLS1

PLS2

Figure 3: Loading biplots for each of the developed models

36 38 40

32 34

24 26 28 30

Without Zone 1 Temperature Fault DOE Run Number

18 20 22

18 20 22

24 26 28 30 32 34 36 38 40

With Zone 1 Temperature Fault DOE Run Number

Model

t2

DmodX

PCA1

t2

DmodX

PCA2

t2

DmodX

PLS1

t2

DmodX

PLS2

Observation Number Observation Number Figure 4: Shewhart Control Charts of t2 and DmodX values for each model The models generally had good sensitivity to faults that were investigated by the training DOE. For example, the models were highly sensitive to the changes in material imposed during runs 23, 24, and 34 by detecting the change in viscosity, pressure, torque, etc. With some exceptions the models also detected changes in air pressure, puller speed, screw speed, and most temperature

shifts. However, the model capability was dependent on the set of included data and type of model. For example, the zone 1 temperature was intermittently cycled a few degrees in run 19. This fault is detected with high DModX values for all four of the models including the zone 1 temperature but none of the four models excluding the zone 1 temperature. The reason

is that the exclusion of this data reduces the observability of the models, such that they have no way of directly detecting if the zone 1 temperature is drifting. It is noted that major variations in the zone 1 temperature will affect the melt viscosity, screw torque, and extrudate quality and so will eventually trigger an alarm. Indeed, this hypothesis is confirmed in run 20 when the zone 1 heater is turned off providing a greater process disturbance that is detected with by DModX values for all four models including the zone 1 temperature as well as a trend in the t2 statistic by the PCA2 model that does not include the zone 1 temperature; the results are similar for run 28 when the zone 1 temperature is run consistently cool. Table 6: Fault DOE and Model Evaluations With Zone 1 Run #: Fault PCA1 PCA2 PLS1 PLS2     18: Center-run     19: Zone2 raised 10 C     20: Die 2 dropped 1 C     21: Thermolator off     22: Feeding issue     23: 75/25 blend     24: Added 5% colorant    25: Water bath gap 5 cm      26: Coolant pump off     27: Center-run     28: Zone 1 dropped 2 C    29: Water level off 1 cm     30: Feed throat bridged      31: Center-run    32: Screw speed +6 RPM     33: Puller set 30 cm/min      34: Different material     35: Center-run    36: Air pressure +3inH20      37: Micrometer +10deg     38: Air disconnected     39: Mandrel retracted     40: Center-run     41: Cut Extrudate # Correct Alarms:  15 18 17 14 # False Alarms:  0 0 0 0 # Undetected Faults:  9 6 7 10 Overall Score 6 7 7 3% 5% 1% 8%

Without Zone 1 PCA1 PCA2 PLS1 PLS2                                                                                                 12 17 14 11 0 0 0 0 12 7 10 13 5 5 7 7 4 0% 1% 1% 6%

Run 22 is a short blip in the screw rotation speed at the end of the extrusion run, which was detected by all the PCA models but none of the PLS models. The reason is that the PLS models have a very different structure that reduces the sensitivity of the screw speed to extrudate quality. Runs 23 and 24 were process faults related to the use of polymers having different viscosities controlled through the blending of two different materials. As with run 22, the PCA2 model proved the most capable in detecting these changes as trend in the t2 and DModX statistics due to the inclusion of virtual process states that explicitly modeled the melt viscosity though the PLS1 model was also found capable. Run 30 was a materialrelated fault in which the screw was starved, which was detected by all eight models. The models had a difficult time detecting physical changes in the extrusion line equipment; these faults

tended to not affect the process dynamics and so were not readily observable from the t2 and DModX statistics. For example, the extrudate was temporarily held in run 27 to cause a blip in the extrudate diameter. This small blip was not sufficient to be outside of specification but was detectable in the DModX statistics in the PLS1 and PLS2 models. By comparison, the extrudate in run 41 was cut between the puller and the optical gauge, but everything was allowed to keep running. Since the cut tube remained on the laser micrometer and the process was operating at the center point, there was no way for the multivariate controller to detect this fault.

Discussion The experimentation and analysis are enlightening in with respect to the relationship between instrumentation and observability. The standard extrusion molder setup of statistical process control of monitoring the die temperature, melt pressure, and screw speed/torque corresponds closely to the PCA1 model. As indicated by the results of Table 6, this level of instrumentation resulted in capturing only 50% of the imposed faults in this study and so is likely to be insufficient for fully automatic quality assurance in practice. The predictive capability of a multivariate quality control approach can be significantly increased by adding additional process signals including, for example, on-line laser metrology of the extrudate, puller speed, environment sensors, and additional die or barrel temperature signals. The reason is that these additional signals increase the observability of the process and the controller’s ability to detect changes in the process states and/or their correlations. With respect to the noisy temperature behavior shown in Figure 2, the results of Table 6 definitively indicate that more data is better. However, the statistical methods must be sufficiently robust to detect the underlying causal relations amidst a noisy signal. Regarding the type of model, the results of Table 6 indicate that causal modeling of the extrudate quality using an advanced method such as Projection to Latent Structures (PLS) may not provide significantly better fault detection than Principal Components Analysis models. The reason is that the PLS models operate on the same dataset, yet may not have sufficient fidelity to predict the extrudate quality with precision. For example, on-line metrology of the inner diameter for medical tubing may not be feasible, yet off-line metrology can be expensive. As such, on-line prediction of tubing diameter would prove highly valuable to the extrusion molder. Figure 5 plots the predictions of the inner tubing diameter for the PLS2 model against their observations. The averages of the predicted and observed inner diameters are equal, yet there is a high degree of variation between the predictions and the observations. There are many possible reasons for the lack of model fidelity including second order interactions, non-linear behavior across the characterization range of the DOE, and others. In any case, the PLS model provides a correlation coefficient of 0.7, which means that 70% of the variation in the observed behavior is explained by the model while 30% of the observed behavior is not explained. If the

specification on the extrudate diameter was 0.85 mm ± 0.05 mm, then the extrusion molder would have to set the limits on the PLS model to either 1) be relatively tight and improperly reject a large fraction of potentially acceptable product, or 2) be relatively loose and improperly accept a large fraction of potentially defective product. The ultimate selection of the control limits (such as those plotted in Figure 4) is made by the plastics manufacturer to balance the cost of rejecting good product with the cost of accepting defective product. 1.1 1.05

Predicted Inner Diameter (mm)

1 0.95 0.9 0.85 0.8 0.75

References

0.7 0.65 0.6 0.6

faults. It is important that the models are developed using data from a complete training DOE that sufficiently probes the process window. It was also determined that the capability of the models is highly dependent on the type of model as well as the type of data being provided. In general, the multivariate models are sufficiently robust such that the inclusion of more data (even very noisy data) will improve the predictive capability of the quality controller. Furthermore, the inclusion of virtual process signals for process states that are not directly observable (such as melt viscosity, draw ratio, specific mechanical energy, and others) significantly improves the responsivity of the models to small process disturbances. While the research indicates that tight control of the extrusion process is possible, the research is not conclusive with respect to the possibility of a universal instrumentation suite and quality control methodology. As such, extrusion molders remain challenged to determine and validate the most optimal instrumentation suites on an application-specific basis.

0.65

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0.75 0.8 0.85 0.9 0.95 Observed Inner Diameter (mm)

1

1.05

1.1

Figure 5: Predicted and observed inner diameters In applications such as medical tubing with a high cost of accepting defective products, the control limits are selected to be tight such that a fraction of acceptable product is improperly discarded. In any case, these compliance costs can be reduced through the use of multivariate control models with improved model fidelity. Reflecting on this extrusion research, the model fidelity and fault detection could definitely be further improved with additional streams of information. Some of the additional data that could include extrudate tension into the puller, water bath position, feedstock temperature, water bath flow rate or pump current, as well as environment temperature, humidity, and pressure. While varying on an application-specific basis, the preceding list is provided in order of decreasing importance. For example, the extrudate tension in combination with online metrology of diameter and line speed would provide valuable information regarding material characteristics. It is interesting to reflect on the relative cost:benefit ratio of the potential implementations. For example, the water bath position was found to be a critical but often loosely controlled determinant of extrudate quality. While sensing the water bath position would be quite costly to implement, the use of a setup fixture or plenum lines on the floor and machinery would allow reasonable control at very little cost. Other control measures on the feedstock and environment can be used to narrow the variability surrounding the extrusion process and are adopted on an as-needed basis. In any case, this research suggests that the extrusion process can be very tightly controlled.

Conclusions Multivariate analysis has been applied to the extrusion process to detect imposed process faults. In a blind validation study, both PCA and PLS models generally did well at detecting and identifying the process

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