【正文】 Fig. 4. Loading plot on the quality variables ( Y’s).tion exists between high preheat temperature and highratio between the master batch and isocyanate (MB/I).This observation can be explained by fact that as thepreheat temperature rises, isocyanate which has alower molecular weight will tend to evaporate andconsequently the ratio of the master batch to isocyanate reacting in the cavity will rise. It is worth notingthat different operators had already observed that, ingeneral, a high temperature resulted in a high kfactor.Fixture 2, on the other hand, exhibited a lowerpreheat, core, and sidewall temperature, in general,and higher isocyanate temperatures. Defective andfaulty heaters in both the mixhead and the preheatstation in fixture 2 were found to be the root cause ofthese correlations.. Projection to latent structure (PLS) betweenprocess and quality variablesA PLS model was then built between the processvariables and the spatially averaged quality variables.The results of the PLS indicate a very strong correlation and a dimensionality of three based on crossvalidation. These three ponents explain 79% ofthe variation of the quality variables. A plot of t1vs.u1(latent vectors in the X and Y space, respectively,for the first ponent) in Fig. 9 shows a very strongrelationship. The loading plot shown in Fig. 10 highlights the important variables in the process and pointsto where the variability in the quality variables ising from.Master batch temperature at mixhead (MB_T_MH), preheat temperature (Preheat_T), shot size,and ambient temperature (A_T) all prove to have apositive correlation with kfactor and the occurrence ofleaks while the isocyanate temperatures (I_T andI_T_MH) showed a negative correlation with kfactoras well as density.The above PLS model only reveals the correlationstructure of the data during routine plant operation,and the observed correlation among the process andquality variables cannot be interpreted as causalF. Yacoub, . MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 17–33Fig. 5. Loading plot for the PLS between the presence of a fixture (x) and the quality variables ( Y’s).23relationships. However, the PLS loading plot in Fig.*10 reveals some very interesting relationships thatneeded to be explored further. Therefore, at this stage,it was decided to proceed with a designed experimentin order to establish causal relationships among thequality variables and some of the more interestingprocess variables arising from the PLS analysis. Theprocess variables chosen were the ones that had a highcorrelation with the quality variables as discoveredfrom the PLS loading and coefficients plot, and werealso capable of being directly manipulated. The ratioof Master batch to isocyanate (MB/I) was set to afixed value suggested by the supplier of the chemicals. Ambient temperature (A_T) was considered as anoise variable that needed to be investigated andeventually controlled if possible.. Response surface model (RSM) developmentIn general, the best way to develop a cause andeffect model and use it to find the optimum conditionsof the process is to design an appropriate set ofexperiments.A central posite RSM design was made inthe following four variables: the shot size (SS) andthe temperatures of Master batch (MB_T), isocyanate (I_T), and mold. The mold temperature used inthe experiment was defined as a weighted averageof the profile of the core, sidewall, and preheattemperatures. The design consisted of a 24fullfactorial with three replicates of each condition, thenthe star points were added to plete a centralposite design. The main objective of runningsuch a design was to identify what variable interactions and curvature terms were important and tooptimize the process by plotting the response surface.By fitting a regression model to the data, the*coefficient of determination R2, which indicate howmuch variation is explained by the model, was %and % for the thermal conductivity and density,respectively. The response surface model resulted in24F. Yacoub, . MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 17–33Fig. 6. t1– t2scores from PCA between the presence of a fixture (x) and the process variables (X’s).Fig. 7. DmodX plot from PCA between the presence of a fixture (x) and the process variables (X’s).F. Yacoub, . MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 17–33Fig. 8. Loading plot for the PCA between the presence of a fixture (x) and the process variables (X’s).*first order prediction equations for both thermal . Multivariate monitoring (MSPC)conductivity and density as follows:25***K factor ? 0:21 ? 0:00064 MB T 0:000778 SS*0:00066 Mold T**Density ? 1:775 0:038 MB T ? 0:0835 SS*? 0:04 Mold TContour plots were then developed for the qualityvariables as shown in Figs. 11 and 12. As shown laterin Section 4, large shot size (SS) has an undesirableeffect on bimetallic bow and leads to a greater use ofchemicals. Therefore, shot size was maintained fixedat a relatively low value that was a promise. Itwas also decided to keep the Mold_T at the lowestsetting as one way to improve energy consumption. It*is then obvious that to minimize kfactor and maximize density, one should increase the master batchtemperature. These conditions were implemented andled to significantly improved panels.The main objective of statistical process control(SPC) methods is to monitor the performance of apro