A Comparison of Statistical Process Control (SPC) and On-Line Multivariate Analyses (MVA) for. Plastics Injection Molding

Transcription

1 A Comparison of Statistical Process Control (SPC) and On-Line Multivariate Analyses (MVA) for Plastics Injection Molding David O. Kazmer, Sarah Westerdale Univ. Mass. Lowell Daniel Hazen MKS Instruments Abstract Manufacturers are increasingly instrumenting their processes for process monitoring and quality control. Many application use statistical process control (SPC) for quality control by charting the process mean and variation relative to defined control limits. The performance of SPC to detect defects is compared to principal components analysis (PCA), which relies on application-specific statistical models. Given these models, PCA track the process variation according by a score of the distance to the model (DModX) as well as the process behavior by the Hotelling t-squared (T 2 ) value. The comparison between SPC and PCA is made with respect to an instrumented injection molding process that is subjected to twelve common process faults. The SPC and PCA models were developed using a design of experiments to ensure consistency. The results indicate that

2 the SPC PCA was able to detect % of the defective moldings caused by the imposed faults as well as % of the defects caused by random process variation. Reflection on the results indicates that the methodology is mathematically rational, but requires upfront investment, careful implementation, and validation on an application

3 Introduction Manufacturing requirements increase, and manufacturers respond by implementing improved manufacturing technologies and processes. With respect to quality, improvements in process sensors, data acquisition systems, actuators, and control logic all ensure the delivery of more consistent products. With respect to economics, these same technology improvements reduce defect costs while also facilitating greater machine productivity. There has been continued interest in process automation for several reasons, including: improved process consistency, improved process productivity, reduced operator fatigue, and reduced labor costs. Yet, automatic quality assurance continues to be a barrier to process automation, especially in plastics manufacturing where part properties are extremely diverse and may be expensive or time consuming to measure. As such, plastics manufacturers continue to rely on operators for process monitoring, product inspection, and fault diagnosis. Yet, the global economy would likely benefit if robust automatic quality control methods could be widely implemented. Statistical process control is a common method for tracking the stability of a process by comparing one or more process states to specified lower and upper control limits. The control chart was first conceived by Shewhart while working for Bell Labs in the 1920s [1]. There have subsequently been many different types of control charts and associated control laws developed for process acceptance or rejection. The most common of these control charts include the Xbar and R chart for tracking the mean and range of smaller populations or sub-groups sequentially produced in a manufacturing process [2]. The X chart is also very common for tracking the process state on an individual sample basis. These chart types can also be used in parallel for tracking multiple process states at

4 the same time, with the process being accepted only when all of the tracked process states are found to be in statistical control [3]. One common issue with the preceding univariate charts is that many charts may be required to successfully track a complex process. Accordingly, multivariate analyses have been developed to track the relationships and variances between multiple process states [4, 5]. Among these multivariate analyses, the CUSUM chart is the simplest and most common [6, 7]. Essentially, the CUSUM chart sums the number of standard deviations of the multiple process states relative to their control limits, and accepts the process only when the sum of all the tracked standard deviations is less than a specified limit. EWMA have been developed that exponentially weight the moving average to provide improved performance for noisy or sensitive systems [8]. On a more advanced level, Hotelling T2 charts have been used to calculate and track the covariances between multiple process states [9]. This type of multivariate method provides greater sensitivity to process changes since it tracks not only the perturbation of the process states from the mean, but also changes in the relationships between multiple process states. Another benefit to these multivariate methods is that they usually provide fewer control limits to track since they consolidate multiple process states into fewer cumulative statistics. Unfortunately, multivariate methods require numerical analysis to develop the correlations and can be more difficult with respect to interpretation of the results. In this paper, four different quality control methods are implemented and compared for an injection molding process. The first two methods are based on conventional statistical process control charts for tracking different process states originating either from the molding machine or the mold cavity. Since SPC is

5 traditionally applied to only the few most important process states, best subset regression analyses [10, 11] were used to select the best process states for SPC to ensure optimal performance. The latter two quality control methods are based on multivariate analyses. The simpler of these two multivariate analyses is principal components analysis (PCA), which introduces new variables called principal components that consist of orthogonal linear combinations of the original variables to model the correlation structure and reduce the redundancy between multiple process states [12]. In addition, projection to latent structures (PLS) is also used to explicitly model and track the correlations structure between multiple process states and measured quality attributes [13]. Methodology The implemented methodology for all four quality control methods is depicted in Figure 1. The input to the methodology is an appropriately instrumented manufacturing process. While injection molding processes vary significantly with respect to structure and operation, the instrumentation needs to provide sufficient observability of the process for an automated system to function. In most molding processes, the instrumentation includes critical timings, pressures, temperatures, velocities, and others. Ideally, each process state is directly related to a specifiable machine set-point to directly support prediction and control of the quality of the manufactured products.

6 Instrumented process Characterize variation Perturb process Modify process Robust? yes Model process no Apply model Accept/reject decisions Figure 1: Implemented control system architecture Given a properly instrumented manufacturing process, the process is set-up and operated at a standard set of conditions that is believed to be most desirable with respect to trading off the multiple quality attributes, yield, time, and costs. The manufacturing process is then operated at these standard conditions in a fully automatic mode per the plant s standard operating procedures. The instrumentation streams process data in real time, which is analyzed to provide information about the states of the manufacturing process. The information for each process state is then statistically characterized with respect to trend, mean, and standard deviation. In the current implementation, Gaussian statistics are assumed though other distributions are admissible. Once the process variation is characterized at the standard conditions, the process is purposefully perturbed according to a design of experiments [14]. There are two reasons. First, the imposed process perturbation bounds the variation that is expected in

7 the long term operation of the manufacturing process. If the quality of the moldings is acceptable at the different perturbations, then the DOE provides confirmation that the standard conditions are robust. If some of the perturbed conditions result in defective moldings, then the molder is informed that their process is not robust, and advised to shift their standard conditions to a more robust region. The second reason for perturbing the process is to induce variance for the statistical characterization of the process behavior. In all four of the implemented methods, the observed variation is used to derive the control limits that are subsequently used for acceptance or rejection of a molding process. The control limits vary by type of analysis. For the conventional statistical process control based on straight charting of the observed process states, the outer limit for process acceptance is set to three times the standard deviations of the process states observed during the perturbation experiment. Process warning limits, indicative of potential changes in the process, were set to two times the observed standard deviations of the process states. In determining these limits, there is a balance between setting too low a rejection threshold and rejecting a high percentage of acceptable products verses too high a rejection threshold and accepting a high percentage of defective products. As subsequent results will show, a rejection threshold of three standard deviations was found to be reasonable. With respect to the multivariate analyses, the control variables and their corresponding limits are not as simply derived from the process states. Instead, both principle components analysis (PCA) and projection to latent structures (PLS) model the statistical relations between the observed process states [15] and, in PLS, the observed states and one or more quality attributes. Both these methods are expected to outperform

8 traditional SPC since a well instrumented process can literally provide dozens or hundreds of data points for each manufacturing cycle; much of the provided data is redundant since it is highly inter-related. Accordingly, PCA and PLS reduce the redundancy by introducing new variables called principal components that consist of orthogonal linear combinations of the original variables. The resulting model will typically have fewer principle components than the original number of process states while explaining more of the observed process variation than a conventional linear regression. In the implemented multivariate methods [12], each column of process data is centered, scaled with respect to the measured standard deviation, and auto-fit with a minimum number of principle components to maximize the explained process variance. Outliers from the initially developed model are identified at the 95% confidence level and removed from the characterization data set. The decision to accept or reject subsequently a molding process is made by testing the statistics from the collected process data against the accepted model for quality prediction. There are two statistics that are useful in summarizing process behavior: the DModX and Hotellings or T 2. The DModX is the residual standard deviation calculated from the residuals, i.e., after subtracting the accepted model behavior from the scaled and centered process data. For an observation to be judged acceptable (non-deviating), the DModX should be smaller than a critical limit corresponding to a 99% or other desired confidence limit, as calculated from the F-distribution [16]. The T 2 value is a second summary statistic that represents the distance of the collected data from that of the standard operating conditions. As with the DModX, an observation is judged acceptable if T 2 value of the collected data is within the confidence intervals of the

9 accepted model [17]. In this research, the supposition is that the T 2 value is indicative of process defects when the observation exceeds the 99% confidence limit. A similar supposition is that large model residuals are indicative of process changes when the observed DModX value exceeds the 99% confidence limit. Experimental The effectiveness of the four quality control methods was experimentally investigated with respect to an instrumented injection molding process that is subjected to twelve common process faults. Not every imposed process fault would necessarily result in a molding defect. The plastic material used was polypropylene (Braskem polypropylene CP201, lot number S) mixed with 10% regrind. A mold for producing ASTM test bars was instrumented with cavity pressure and temperature transducers as shown in Figure 2. Two unshielded cavity thermocouples were located near the end of fill and four piezoelectric pressure transducers were located near the sprue and gate locations. The molding process was also instrumented with a nozzle pressure transducer, ram position transducer, ram load transducer, cycle timers, coolant thermocouple, four barrel thermocouples, room temperature sensor, and relative humidity sensor. From these sensors, a set of forty four process states were calculated for each molding cycle and provided for the described principle components analysis.

10 CP: Cavity Pressure Sensor CT: Cavity Temperature Sensor Step Plaque CP CP CP Tensile Bar CT CT Flex Bar CP Figure 2: Molded test specimens showing instrumentation and measurement locations Experiments were performed with an all electric 50 metric ton Ferromatic Milacron machine. A commercial auxiliary controller (MKS SenseLink) was used for data acquisition, analysis, and quality control. A set of one hundred molding cycles were consecutively run to statistically determine the mean and standard deviation of the molding process at standard conditions. Next, a design of experiments (DOE) was developed to characterize the process behavior expected across a long term production run. To simulate long term process variation, the standard process conditions were perturbed by six standard deviations ( 6 ) of their measured variation. This magnitude of variation was selected to emulate the long term variation of the machine, material, and operator in a production environment [18]. For example, the plasticizing stroke was initially set to 85 mm and subsequently observed to have a standard deviation of 0.3 mm across the hundred consecutive molding cycles. The expected magnitude of long term

11 variation is or 1.8 mm, so the minimum and maximum value for the plasticizing stroke was set to 83.2 and 86.8 mm in the characterization DOE. The implemented characterization DOE is shown in Table 1. A fully saturated design of experiments, 2 7-4, was used in this study to perturb seven of the most significant process settings in only eight runs; this DOE is sufficient for characterizing the mean and linear main effects, but all interactions are confounded [14]. The standard process setting, run 0 of the DOE, was also added to expand the data set and verify linearity. After the process reached equilibrium for each run in the DOE, the data and molded products from ten manufacturing cycles were collected using a fully automatic production mode to ensure process consistency. Table 1: Characterization DOE DOE Run # Plasticising stroke (mm) Injection speed (mm/s) Pack pressure (bar) Cooling time (s) Barrel Temp (C) Coolant Temp (C) Regrind Level (%)

12 SPC can not practically be done with all 44 process state since it would be highly burdensome and also provide a high proportion of falsely rejected products. To identify the most appropriate process states to perform the conventional SPC methods, best subset analyses were performed. In this statistical analysis, a series of multiple linear regressions were used with different combinations of process states to identify the optimal number and selection of process states. Two different sets of process states were analyzed. First, a set of 25 process states consisting only of data from machine sensors was analyzed. The results are in Table 2 and indicate which process states provide the best statistical correlation with the measured part width. If only a single variable is used, then coolant temperature was found to be the best predictor with a regression coefficient of 38%. As the number of process states increases, different process states are included in the model and provide an improved statistical correlation. Table 2: Best subset analysis for SPC with machine variables

13 Fill Time Pack Time Recovery Time Cool Time Cycle Time Screw Displacement Filling Screw Displacement Packing Screw Displacement Cooling Fill Speed Velocity at Transfer Packing Velocity Velocity during Recovery Max Fill Pressure Avg InjPressure Filling Hold Pressure Back Pressure Injection Energy Recovery Energy Melt Visc during filling Melt Visc during packing Avg Nozzle Temperature Avg Metering Temperature Avg Feed Temperature Avg Coolant Temperature Cushion Shot Size # Vars R 2 R 2 adj Mallows CP In Table 2, the Mallows CP is an indicator of the remaining process variation relative to the average variation explained by the included process states. Mallows [11] suggests that overfitting can be avoided when the number of included process states is between one and two times the calculated CP value. For this reason, five process states were selected from the best subset analysis: average coolant temperature, melt viscosity during filling, injection energy (the integral of injection pressure with respect to screw displacement), maximum filling pressure, and the filling speed. The regression coefficient indicates that 78.7% of the observed process variation in the perturbation DOE was explained by this model. There has been significant discussion in the industry about the selection and use of in-mold process sensors for process control. Accordingly, process states from in-mold

14 Fill Time Pack Time Recovery Time Cool Time Cycle Time Screw Displacement Filling Screw Displacement Packing Screw Displacement Cooling Fill Speed Velocity at Transfer Packing Velocity Velocity during Recovery Max Fill Pressure Avg InjPressure Filling Hold Pressure Back Pressure Injection Energy Recovery Energy Melt Visc during filling Melt Visc during packing Avg Nozzle Temperature Avg Metering Temperature Avg Feed Temperature Avg Coolant Temperature Cushion Shot Size Max Runner Pres Max Pressure in Flex Max Temperature in Flex Integral Pressure in Runner Integral Pressure Flex Integral Temperature Flex Time Max Pressure Runner Time Max Pressure Flex Time Max Temperature Flex Time Pressure Runner Decays 70% Time Pressure Flex Decays 70% Time Pressure Runner Rises Time Pressure Flex Rises Time Temperature Flex Rises sensors were derived and another best subset analysis was conducted for a superset of process states that also included the process states from the machine signals identified in Table 2. The resulting best subsets are shown in Table 3. The results indicate that 78% of the process variation can be explained by only three variables: integral of the pressure in the flex bar mold cavity, maximum temperature in the flex bar cavity, and melt viscosity during filling. Furthermore, the analysis indicates that the process states derived from the in-mold sensors are consistently preferred over the machine variables with respect to predicting the variance in the molded part quality. This information is of significant practical value to industry practitioners, and will be subsequently verified with results from later SPC charts. Table 3: Best subset analysis for SPC with mold and machine variables # Vars R 2 R 2 adj Mallows CP For the multivariate analyses, it is unnecessary to select a subset of the process states for analysis. Rather, the PCA and PLS analyses are applied to all of the data collected from the ninety molding cycles of the perturbation DOE, with each cycle being represented by a vector of 44 process states. The first principle component alone models

15 approximately 52% of the process behavior while the first and second principle components together modeled approximately 74% of the process behavior. While both PCA and PLS can use many principle components, only two principle components were used to avoid overfitting the model. The loadings scatter plot provided in Figure 3 plots the contribution of each process state to these two principle components. In this plot, the contribution of each process state has been scaled relative to the total variance explained by the principle component. The plot indicates the correlation of the various process states to the first two principle components, with process states further from the origin having greater correlation. The plot is also useful to indicate the correlation of each process state with respect to other process states. For example, the upper right quadrant indicates that the flex bar width is well correlated with the hold pressure, maximum runner pressure, and screw displacement during cooling. The default values for the Hotelling T 2 and DModX values at the 99% confidence level were taken as the control limits for both types of multivariate analyses.

16 Figure 3: Loadings scatter plot for first and second principle components The capability of each of the four different models was validated by purposefully imposing twelve process faults that are common in injection molding operations. The twelve faults are listed and described in Table 4. Prior to each fault, the process was allowed to stabilize at the standard operating conditions of run 0 in Table 1. Five cycles of data were then procured at the standard operating condition after which the fault would be incurred and the data from the cycles with the faults collected as described in Table 4. Not all of these faults resulted in moldings that did not meet tolerance specifications. In

17 the next section, the results from each of the four with respect to identifying which of the molding cycles were faulty and also which of the moldings were defective. Table 4: Imposed process faults Process Fault Description Collection Plan Contributing process states Coolant temperature controller off The coolant temperature controller was turned off while the machine continued to cycle. Every fifth cycle collected after the fault was imposed. Coolant temperature; time for pressure decay Wrong material The material in the hopper was replaced with a similar appearing material, high impact polystyrene (HIPS). Several cycles were run to assure that the resin consisted only of the new material, after which five consecutive cycles were collected. Plastication time, fill pressures Wrong percentage of regrind The material in the hopper was replaced with 100% regrind as opposed to the specified amount of 10%. Several cycles were run to assure that the resin consisted only of the new material, after which five consecutive cycles were collected. Melt viscosity; plastication time Barrel temperature adrift +20C The nozzle temperature was increased to 20C above the standard setting. Every fifth cycle collected after the fault was imposed. Nozzle temperature; time for pressure decay Cavity closed The step plaque cavity was shut off with the injection pressure was limited to avoid damaging the mold. Process data from five consecutive cycles were acquired immediately. Filling time; filling pressures Nozzle drool prior to injection The plastication unit was withdrawn from the mold to allow polymer melt to drool from the nozzle. Process data from five consecutive cycles were acquired immediately. Screw displacement during filling Idle machine The standard molding process was stopped (with a full shot still in the barrel) and allowed to idle for 10 minutes. After the delay, the machine resumed its base process for five cycles of which the first cycle was collected. Five fault cycles were sampled in this manner. Cycle time; time for pressure decay Cold feedstock The resin (PP 10%RG) was placed in a freezer at -20C for 36 hours. Several cycles were run to assure that the resin consisted only of the new material, after which five consecutive cycles were collected. Melt viscosity; time for pressure decay Low packing The pack time was Process data from five Screw displacement

18 pressure/time decreased from 15 seconds to 5 seconds and the pack pressure was decreased from 200 bar to 100 bar. consecutive cycles were acquired immediately. during packing; time for pressure decay Excessively short cycle time Cooling, packing, and plastication time were reduced by ~50%. Process data from five consecutive cycles were acquired immediately. Cycle times; cushion Low cushion The switchover point for the faulty process was decreased to reduce the material in the barrel. Process data from five consecutive cycles were acquired immediately. Cushion; shot size; velocity after filling Cold Machine The machine was turned on after twelve hours of nonoperation, and cycles were performed as soon as safely possible. Process data from five consecutive cycles were acquired immediately. Barrel temperatures; melt viscosity Results The most conventional application of statistical process control to injection molding is the charting of data from machine sensors. The best subset analysis indicated that the best statistical correlation with part width was achieved with a model including the fill speed, maximum injection pressure, injection energy, melt viscosity, and coolant temperature. The upper and lower control limits (UCL and LCL) for each of these five process states was calculated as the observed mean plus and minus three observed standard deviations from the perturbation DOE of Table 1; moldings from any cycle with a process state outside these control limits are assumed to be defective. The observed process states and the resulting control limits correspond to cycle numbers 1 to 90 in Figure 4. It is observed that there are different steps in the process states, corresponding to the different run conditions in the DOE. However, all of the cycles in the DOE (number 1 to 90) are within the LCL and UCL.

19 Figure 4: Statistical process control charts for machine states The control charts of Figure 4 also include dashed lines corresponding to two standard deviations in the process states from their mean in the perturbation DOE; any molding cycles outside these warning limits are assumed to correspond to a significant process change, but not necessarily to produce defects. For example, cycles 16 and 17 in Figure 4 are marked with a square to indicate that the maximum injection pressure and injection energy are below their lower warning limit. These cycles correspond to run 1 of the DOE in Table 1, which has a reduced plasticizing stroke, higher barrel temperature, lower filling speed, and higher mold temperature. These settings are an extreme condition since they all tend to reduce the injection pressure and energy. Accordingly, the cycles at these conditions trigger the warning limits but do not violate the outer control limits.

20 Cycles 91 to 215 of Figure 4 correspond to five molding cycles operated at standard conditions (run 0 of Table 1) alternating with five cycles operated the various faults (sequentially described in Table 4). A close inspection of Figure 4 indicates that twenty one molding cycles fall outside the outer control limits and are assumed to have produced defects. For example, 106 to 110 indicate the molding should be rejected due to an excessive injection pressure, injection energy, and melt viscosity. These unacceptable process states are, in fact, due to the use of a similar appearing high impact polystyrene (HIPS), which does result in defective moldings. The performance of these control charts based on the process states measured by machine signals will be later compared to the other SPC and multivariate methods. Injection molding machinery has become increasingly integrated with in-mold cavity sensors. The best subset analysis including all available machine and in-mold process signals resulted in a model including melt viscosity, maximum temperature in the flex bar cavity, and integral of the injection pressure in the stepped plaque cavity. The control limits for these process states was similarly set to three standard deviations from the mean during the perturbation DOE of Table 1. The resulting control charts are provided in Figure 5. While Figure 5 (based on in-mold signals) is very similar to Figure 4 (based on the machine signals) and both control charts indicate twenty one rejected molding cycles, the two sets of rejected cycles are not identical. The performance of both these conventional control charts will be later compared to the multivariate methods.

21 Figure 5: Statistical process control charts for in-mold states Principle components analysis provided a model based on the perturbation DOE of Table 1. The resulting Hotelling T 2 values can calculated for any of the principle components and subsequently used as indicators of process variance; the residuals (DModX) can also be used as an indicator of changes in the molding process. These indicators are plotted in Figure 6 with their corresponding control limits set to the 99% confidence limits. While these indicators are not as directly interpretable as the univariate process states previously charted, they can be directly used for cycle acceptance. In Figure 6, excessive T 2 values for the first and second principle components are assumed to produce defects (marked with an x ) while excessive residuals are assumed to indicate a process change (marked with a ). It is observed that the set of rejected molding

22 cycles is somewhat different from those based on conventional SPC. Furthermore, it is observed that the model residuals indicates many process changes than the previous control charts. Figure 6: Statistical process control charts for principle components analysis Projection to latent structures (PLS) correlates the observed variance in the process states to observed variance in the measured part width. PLS is the only method that required measurement of the molded samples prior to model creation and establishment of the corresponding control limits. Subsequently, the molded parts were rejected based solely on process data in an automatic fashion. The control charts for the PLS analysis are provided in Figure 7. Comparing Figure 7 to the previous control charts, it is observed that the PLS accepts all ninety cycles from the perturbation DOE while all

23 the previous methods rejected several cycles corresponding to run 1 of Table 1. Subsequently, PLS provides predictions very similar to PCA though the two sets of predicted defects and process changes are not identical. Figure 7: Statistical process control charts for projection to latent structures To provide a direct comparison of the process change predictions, Figure 8 plots the sequence of imposed process faults as well as the predictions of process changes from the various analyses. The upper graph of Figure 8 shows the cyclically imposed process faults from cycles 95 to 215; the lower graph indicates that the various methods have predicted a process changed when the indicator is high. It is observed that the multivariate analyses are much more sensitive in predicting process changes.

24 Specifically, both the PCA and PLS analyses predicted ten of the twelve imposed faults while the SPC charts based on either mold or machine signals both predicted only five of the twelve process faults. All of the methods predicted at least one process change during the perturbation DOE. These results are summarized in Table 5. Figure 8: Comparison of predictions for process changes Table 5: Comparison of predictions for defective moldings # Changes Detected # False Positives # Undetected Changes Ideal Machine SPC Mold SPC PCA PLS

25 Not all of the imposed process changes will result in defective moldings since the variation in the molded part width will vary with the nature and magnitude of the process change. To validate the predictive performance of the various methods with respect to part quality, the molded parts were allowed to equilibrate and subsequently measured. The control limits for the dimensions were then set to three standard deviations from the mean observed during the perturbation DOE. The control charts for the part width are provided in Figure 9 with the observed and predicted defects. A close inspection of Figure 9 indicates that there are twenty four defects use of the wrong material (cycles 106 to 110), blocking one of the cavities (cycles 136 to 140), low packing pressure/time (cycles 176 to 180), excessively short cycle time (cycles 186 to 190), and low cushion in the barrel (cycles 196 to 200). Cycle 182 was observed to be a defect though operated at standard conditions of run 0 in Table 1.

26 Figure 9: Comparison of predictions for defective moldings***rerun no defect at cycle 99 The lower graph of Figure 9 indicates the rejections predicted by the various methods corresponding to the control charts of Figures 5 to 8; the predictions are summarized in Table 6. Generally, the methods have done surprisingly well. Ideally, all twenty four of the defective cycles would be rejected with no false positives. While the specifics varied by method, the conventional SPC based on either the machine or mold signals both failed to detect six of the defects. In terms of false positives, the machine based SPC falsely rejected cycle 98 and cycle 198. While these cycles did correspond to imposed process faults, the measured parts were within the specified tolerance range. While the mold-based SPC falsely predicted only one defect, this is fundamentally due to

27 its inability to predict defects caused by low cushion in the barrel (cycles 196 to 200). Compared to conventional SPC, both multivariate methods caught twenty three of the observed twenty four molding cycles producing defects; the only missed defect was cycle 182, which was observed to be a defect even though the machine was operated at the standard conditions of run 0 in Table 1. Both of the multivariate methods provided false positives for cycle 198 while the PCA analysis also return a false positive for cycle 98. Table 6: Comparison of predictions for defective moldings # Defects Detected # False Positives # Undetected Defects Ideal Machine SPC Mold SPC PCA PLS Discussion Injection molders must have robust and automatic quality assurance methods to attain fully automated molding operations. Statistical process control is a simple and useful tool for tracking important process states to indicate process stability and identify unacceptable molding cycles. The successful application of SPC depends on the selection of the process states to track and the setting of the corresponding control limits. A capable molder with deep application expertise may be able to extract significant value from SPC.

28 This study, however, suggests that there are at least two critical benefits of the described multivariate analyses compared to traditional SPC. First, the multivariate methods provide a fully automatic method for generation of highly capable applicationspecific models and control limits. The presented results for the SPC methods were developed using process states chosen from best subset analyses based on the perturbation DOE from Table 1. In general industry applications, the set of process states to be tracked and their corresponding limits will not be as capable especially since the best SPC model will vary according to the application s geometry, material, and process conditions. By comparison, the multivariate analyses will consider all the process states and generate the principle components to best model the application s behavior. Corresponding control limits are also automatically generated at specified confidence levels. The second advantage of the multivariate methods is increased prediction capability due to the derived application-specific models. Conventional SPC directly tracks important process states, but 1) ignores many other less important process states and 2) fails to track the relations between the process states. By contrast, the multivariate methods track all the process states such that a significant change in a less important process state can trigger significant variance between an observed process and the expected process. Similarly, the multivariate methods track the relationships between all the process states such that a process change may be identified even when all the process states have not significantly changed. Indeed, the results suggest that the model residual (indicating relative changes between the process states) is a powerful indicator of process changes even more so that the changes in the process states themselves.

29 The multivariate analyses are significantly more complex that conventional SPC, and do require numerical implementations for the development of the models as well as the interpretation of the on-line results. Yet, the complexity and robustness of the implementation are not significant relative to the computational power available in industrial controllers. Furthermore, the cost of the multivariate implementation is recouped given the model s increased capability when diagnosing process faults. Consider, for example, the screen image shown in Figure 10, which displays the cycle by cycle trend of the molding process as it goes outside the control limits when the coolant controller is shut-off. While there is no control chart for coolant temperature as shown in Figure 5, the process operator can simply read the model residual (DModX) to recognize that the coolant temperature is decreasing below the standard setting and know to check the status of the coolant temperature controller. Figure 10: Screen image showing the effect of shutting off the coolant temperature controller If there is one issue with the dependence on an application-specific multivariate model, it is the robustness of the developed process models to extrinsic variable. As stated in the experimental section, the deployed process model was based on a

30 perturbation DOE with ninety molding cycles, each with 44 process states. This set of data provided the multivariate analyses with variance in the process states to derive the principle components that correlate the multiple process states. If a process state does not exhibit any variation, then it will not be appropriately included in the process model when the data set is centered and normalized. Later, the developed model can be rendered invalid if the process state subsequently varies even slightly. A such, it is highly recommended that all significant process states (including all those related to environment, machine, and feedstock) be statistically analyzed and perturbed to develop a robust process model. Conclusions Four different quality control systems were implemented: 1) conventional SPC based on machine signals, 2) conventional SPC based on mold signals, 3) principle component analysis of all process states, and 4) projection to latent structures based on process states and measured part width. All four methods used a nine run perturbation DOE to derive their models and control limits. For the conventional SPC methods, best subset analyses were used to identify the set sets of process states to explain the variance in the measured part width. The multivariate analyses used the same data set to derive the principle component analyses and their corresponding limits for the Hotelling T 2 and model residuals (DModX) at the 99% confidence level. Twelve different process faults were imposed on the molding process, of which five of the faults resulted in the production of twenty four defective moldings. Generally, SPC using signals from in-mold sensors slightly outperformed SPC using only machine

31 signals. As might also be expected, the PLS model slightly outperformed the PCA model. However, the both multivariate analyses both outperformed both SPC analyses. Both conventional SPC methods only detected five faults, while the multivariate methods detected ten faults. In terms of prediction of defects, the conventional SPC methods detected eighteen defects, while the multivariate methods detected twenty three defects. The multivariate analyses are highly rigorous and provide significant benefits related to automatic development of application-specific models, increased predictive accuracy, and increased fault diagnosis. The increased capabilities of the multivariate analyses come at a cost premium compared to conventional SPC. Specifically, the multivariate analyses require a numerical implementation and a more advanced user interface. However, the cost premium associated with such an implementation is decreasing with the increasing sophistication of manufacturing technology. Eventually, a majority of manufacturing controllers may embody multivariate analyses to leverage the volumes of available process data, achieve automatic quality assurance, and assist the operator in diagnosing and optimizing their molding processes. References [1] W. A. Shewhart, Statistical Method from the Viewpoint of Quality Control: Dover Publications [2] E. D. Castillo, J. M. Grayson, D. C. Montgomery, and G. C. Runger, "A review of statistical process control techniques for short run manufacturing systems," Communications in Statistics-Theory and Methods, vol. 25, pp , [3] Z. Wu, "An Enhanced X Chart for Detecting Mean Shift," Quality Engineering, vol. 7, pp , [4] C. A. Lowry and D. C. Montgomery, "A review of multivariate control charts," IIE Transactions, vol. 27, pp , [5] T. J. Harris, C. T. Seppala, and L. D. Desborough, "A review of performance monitoring and assessment techniques for univariate and multivariate control systems," Journal of Process Control, vol. 9, pp. 1-17, 1999.

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