Univariate Statistical Process Control Biology Essay

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The methods of univariate statistical process control and multivariate statistical process control and comment on their use in continuous and batch chemical/manufacturing processing

Statistical methods for determining changes in industrial processes is present in a field generally known as statistical process control (SPC). The most widely used and popular SPC techniques involve univariate methods, that is, observing a single variable at a given time as well as statistics, such as mean and variance, that are derived from these variables. Univariate methods are proven, simple, and easy to implement, which is the primary reason for their widespread popularity. However, univariate methods are having some limitations

bivar

While a univariate approach may well indeed work for monitoring a small number of process variables, current trends in data acquisition hardware allow a large number of variables to be easily measured and application to larger multivariable systems becomes difficult, if not impossible, with univariate methods. This simplified approach to process monitoring requires an operator to continuously monitor perhaps dozens of different univariate charts, which substantially reduces his ability to make accurate assessments about the state of the process.

Multivariable statistical process control (MSPC) techniques have been developed to reduce the burden of manually measuring a large number of process variables as well as to provide more robust monitoring methods. MSPC methods are typically concerned with measuring directionality of data from a multivariable spaceas opposed to univariate methods that only monitor the magnitude and variation of single variables. MSPC techniques reduce the amount of raw data presented to an operator and provides a concise set of statistics that describe the process behavior. A balance between MSPC and univariate SPC tools is therefore required to extract the most useful information from a process.

Data-driven MSPC methods that are capable of handling correlated data include Principal Component Analysis (PCA), Projection to Latent Structures (PLS), and Canonical Variate and Subspace State Space modelling. Data-driven techniques are dependent on data collected from a real process in order to formulate a model that describes the variability of that process. This method is referred to as system identification. Conversely, model-based techniques are dependent on detailed physical models of the system of interest. With either method, a model may be used to predict the future values of monitored process variables. Many systems of interest in chemical engineering exhibit non-linear behaviour, thereby mandating the use of linear methods as a close approximation to the non-linear behaviour of the system to achieve meaningful results. After a good model of the process is obtained, one-step-ahead predictions of the process variables may be used to monitor the process. Assuming that the model accurately describes the NOC of the process, one may examine the difference between the one-step-ahead model prediction and the actual value once it is obtained. This difference is referred to as the model residual. Errors between the predicted and actual values may be measured for statistical significance and suggest the presence of abnormal conditions in the process.

In addition to measuring the magnitude of the residuals, one may also examine trends in the residuals. Sensor errors in the form of a bias change, drift, or excessive noise may be diagnosed by examining the residuals over time. Gross sensor failures are easy to recognize using univariate methods and redundant sensor measurements. Slow drifts or failure in one or more sensors, however, are exceedingly difficult to detect via univariate techniques. Periodically performing sensor audits, that is, examining the residuals for statistically significant changes,can greatly enhance the credibility of the data as well as significantly reduce the number of false alarms.

batch

Multivariable Batch Process Modeling, Monitoring, and Fault Diagnosis

Batch and semibatch reactors are frequently used in the pharmaceutical production industry. The characterization of successful batch production implies that a prescribed sequence of process events was executed under quality constraints. Batches vary as a result of disturbances, a lack of on-line quality measurements, acceptable recipe changes in normal operation, and varying batch run lengths. The traditional techniques used in process monitoring apply a combination of mathematical models (Kalman filters) and knowledge-based models (processevaluators based upon statistically-framed models) with varied success in an on-line framework.

The use of nonlinear models allows one to determine product quality during a particular run and if sampling product throughout the course of the reaction is feasible, the quality assessment may leave an indication on how to change the process to regain control. This requires a general differential model between the values and trends of the manipulated inputs and the product quality variables so that when the monitored inputs are outside normal behavior, the product quality variables (if they could be measured) would confirm the observation of abnormal behavior.

The specific purpose of this research is to investigate the merits of utilizing a differential technique and hidden Markov models (HMM) in monitoring and analyzing the operation of a modeled penicillin fermentor. Differential examination is a statistical tool where a set of mathematical basis functions approximates the differential behavior contained within replicates of sequential observations. This has an important link to principal components analysis (PCA), and its use enhances the control chart performance in future data reconstruction. In conjunction with hierarchical PCA (HPCA), where the complete data trajectory is not required for classifying the overall status of the current batch run, differential techniques allow for effective process characterization by a few user-friendly monitoring charts. Partial Least Squares (PLS) in conjunction with an extended Kalman Filter (EKF) framework allows final product quality estimates to be made with the insight of optimal control moves included. Applying differential estimation techniques to the PLS/EKF framework will further improve final product quality prediction.

Dynamic time warping (DTW) is a fault diagnosis tool, and the more flexible hidden Markov modeling will be implemented. Hidden Markov modeling is a stochastic tool where a series of observations are approximated as sequence of chain events linked by transition probabilities. DTW is also a tool utilized to align similar events within batch trajectories. Optimal curve registration will be applied to illustrate the added benefit of applying PDA to align batch processes of multiple phases. The system of tools can be utilized to form a supervisory framework that would operate on-line in the fault detection, diagnosis and overall supervisory control of a batch system.

USES

The primary objectives of MSPC are to provide early warning of changes in process behaviour and the assured manufacture of consistent production. Additionally, through a deeper understanding of the process a reduction in raw materials usage and levels of rework and waste are achievable, and as a consequence a minimisation of the impact of the process on the environment. These objectives can be realised through the monitoring of the performance of the manufacturing process over time and ensuring that it remains in a "state of statistical control". When the process moves outside the desired operating region, it is regarded as being "not in a state of statistical control" and it is necessary to alert plant operational personnel that a change in process behaviour has occurred, as well as provide them with appropriate diagnostic information about the process variables causing, or reflecting, the problem, thus enabling corrective action to be implemented.

The availability of cheaper and more robust sensor technology has resulted in industrial processes becoming more extensively instrumented with the resulting measurements being recorded routinely on data acquisition systems. A consequence is that the implementation of standard univariate statistical process control techniques to such processes is limited in terms of applicability. Firstly, operators can only monitor and respond to signals from a few charts and thus the majority of process measurements recorded tend to be ignored. Linked to this is that the process measurements recorded are not independent. Univariate SPC only considers deviations from the desired target value and does not take into account the inter-relationships that occur between the variables and thus, valuable process information concerning the behaviour of the process is ignored. In practice, under normal operating conditions, a few combinations of the process variables determine the performance of the process at any one time and influence product variability. The projection based technique of principal component analysis (PCA) is a method particularly suited to analysing data sets comprising correlated and collinear variables [1]. The methodology projects the process data down onto a low dimensional subspace, through the definition of latent variables, and in this way the major sources of variability associated with the process are summarised. The latent variable space is defined by the span of the eigenvectors (principal component loadings) of the sample variance-covariance matrix of the data set. The individual latent variables, which are themselves orthogonal, are linear combinations of the original process variables. Future process measurements are then projected down onto the subspace (principal component score-space) to monitor the behaviour of the manufacturing process. When an "out of statistical control" signal is detected, relevant information concerning the combination of variables indicative of non-conforming operation can be found by interrogating the contribution of each process variable to the principal component score.

Reported practical applications of multivariate statistical process control have focused upon the production of a single manufactured product. That is, one product grade or one recipe with separate models being used to monitor different types of product. However, process manufacturing is increasingly being driven by market forces and customer needs and perceptions, resulting in the necessity for flexible multi-product manufacturing. This is particularly the case in the manufacture of products such as household goods, speciality chemicals, etc. where new product formulations are required to be introduced to the market over a short time scale to ensure competitive advantage. This results in constraints being placed upon the time available between product inception, pilot plant experimentation, laboratory development and factory production. The development of process monitoring models in this kind of manufacturing environment necessitates the use of empirical based techniques as opposed to first principles models since phenomenological model development is unrealisable in the time available. The potential of existing MSPC methodologies for process performance monitoring has been limited by its inability to handle more than one recipe/grade. There is, therefore, a need for methodologies from which process representations can be developed which simultaneously handle a range of products, grades or recipes. An extension to PCA is proposed which allows the development of a multi-group process representation that overcomes the problem of having a single model for every product in a manufacturing portfolio. The method is based upon the assumption that a common eigenvector subspace exists for the variance-covariance matrices of the individual product grades or recipes, and through a pooled sample variance-covariance matrix the principal component loadings of the multi-group model can be calculated.

The method is illustrated through the development of a multi-group model for the monitoring of a commercial semi-discrete batch manufacturing operation, which involves the production of a variety of products (recipes), some of which are only manufactured in small quantities. The different recipes contain a number of similar raw materials, as well as several ingredients that are specific to a particular recipe. By grouping the recipes into a number of sub-groups (families), separate monitoring schemes for each family can be developed. The advantage of this approach is that instead of developing a separate model for each individual product type, which would result in a large number of models, a multi-group model is built for each family. The multi-group model methodology provides a new approach for the monitoring of a large number of products through a limited number of process representations.

2.0 How would you justify to your technical manager and business manager the importance and need for statistical process control.

Importance

Statistical process control help to solve the challenges facing the process industries is the tool use to meet the requirement to ensure the manufacture of consistently high quality products.

It is particularly important in highly demanding situations where manufacturing processes are subject to varying raw material properties, changing market requirements, process specifications and fluctuating operating conditions due to equipment or process degradation. In highly competitive global markets, there is a real need to minimise operating costs, reduce levels of re-work whilst ensuring that variability inherent to the process is minimised.

It is intelligent supervisory systems that not only provide early warning of changes in process behaviour such as the onset of process upsets, equipment malfunctions or other special events, but which can also contribute to the identification of the location of the assignable causes of these events

MultivariatemStatistical Process Control (MSPC). MSPC is increasingly being recognised as a valuable tool for providing early warning of process changes, potential plant faults, process malfunctions and process disturbances and also for enabling a deeper understanding of the process to be achieved.

The methodology is equally applicable to continuous and batch processes and has been investigated by a the primary objectives of MSPC are to provide early warning of changes in process behaviour and the assured.

3.0 Where do you see the problems of applying SPC (univariate/multivariate) in the process/manufacture industries?

Univariate SPC

Univariate SPC looks at the magnitude of the deviations in each variable independent of the other variables; Modeling by PCA and its extensions is done at a single scale. that is, the model relates data represented on basis functions with the same time-frequency localization at all locations.

For example, PCA of a time series of measurements is a single-scale model since it relates variables only at the scale of the sampling interval. Such a single-scale modelling approach is appropriate if the data contains contributions at just one scale. Unfortunately, data from almost all practical processes are multiscale in nature due to Events occurring at different locations and with different localization in time and frequency.

Stochastic processes whose energy or power spectrum changes with time and/or frequency. Variables missing data. Consequently, conventional PCA is not ideally suited for modeling of most process data. Techniques have been developed for PCA of some types of multiscale data such as missing

data, but the single-scale approach forces data at all scales to be represented at the finest scale, resulting in increased computational requirements.typically,monitored process/quality variables are not independent.

The measurements are simply different reflections of the same underlying events

Only a few underlying events are driving the process at any single time

A consequence of examining one variable at a time is that the level of control that can be exercised over the quality and consistency of the final product is restricted and plant flexibility impaired

MULTIVARIATE SPC

Another shortcoming of conventional PCA and its extensions is that its ability to reduce the error by eliminating some components is limited, since an imbedded error of magnitude proportional to the number of selected components will always contaminate the PCA model (Malinowski, 1991). This limited ability of PCA to remove the error deteriorates the quality of the underlying model captured by the retained components, and adversely affects the performance of PCA in a variety of applications. For example, in process monitoring by PCA, due to the presence of errors, detection of small deviations may not be possible and that of larger deviations may be delayed. Similarly, contamination by the imbedded error also deteriorates the quality of the gross-error detection and estimation of missing data. Consequently, the performance of PCA may be improved by methods that allow better separation of the errors from the underlying signal.

4/State how you would proceed in terms of training operators in the techniques requires implementing univariate statistical process control on a process

The first steps is the pre-screening part

. Input of raw data matrix (as collected by the data acquisition system(s)), specification of the process (input) and quality (output) variables including identification of the measurement technique, accuracy of the instrumentation, response time of the measurement, whether the data acquisition system has pre-filtered the variables, etc., and the identification of computed/inferred variables.

. Detection and handling of incomplete/missing information. This stage involves the investigation of whether a pattern is exhibited by the missing data, i.e. is it missing at random (MAR) or not missing at random, e.g. has the instrument reached saturation or has a sensor failed. Depending upon whether the data is MAR or otherwise, the next stage is to select the appropriate algorithm for handling the data. A number of alternative approaches can be tried at this stage such as data deletion or linear interpolation.

. Graphical presentation of the data e.g. time series plots, histograms, scatter plots, principal components analysis, etc. can help identify whether the data is noisy, contains questionable points, is normally distributed, etc.

The resolution of questionable observations, identified from Step 3, through the conjunction of engineering and statistical knowledge.

The calculation of summary information e.g. mean, median, maximum, minimum, range, skew ness, kurtosis, correlation coefficients, etc.

. Test of the variance for single variables and the possible elimination of uninformative measurements.

The removal of unusual noise effects without affecting the signal.

Data alignment through time-shifting variables which exhibit delays.

The identification and elimination of redundant variables by utilising the results from the correlation and principal component analysis.

Mathematical transformations for variables exhibiting non-linear relationships or non-normal behaviour

6222Multivariate statistical

The next steps after the pre-screening stage is to develop the process representation or model using the statistical projection techniques of principal components analysis (PCA) and projection to latent structures(PLS) which are;

Data that encapsulate normal process behaviour is collected (i.e. when the process was operating in a state of statistical control) and it is uploaded as the nominal data.

Principal component analysis is applied to the nominal data set comprising fifteen process variable.

A considerable amount of PCA that explain large percentage of variability more than 80% of the total variability need to be retain

Make the analysis of the

Plots of time series of individual process score.

Bivariate plots of time series of individual process scores

Plot of the T 2of the process scores or plots of the D-statistic time series.

Define the limits of the common cause variation present in the process.

Action limits (Indicate something has gone wrong with the process.

Immediate corrective action required.

Warning limits (Indicate that something may have gone wrong with the process.

No immediate need for corrective action required.

Time series plot of quadratic residuals, in term of the Squared Prediction Error (SPE).

G

BARTII

PROCEDURE/STEPS FOLLOWED WHEN IMPLEMENTING MONITORING PROCEDURES ON THE SPRAY DRY TIME

Step 1 Open the nominal data set i.e. data from which the process representation is to be built

Click on file

Open Nominal

Common on Shark [v:]

files\Prof martin\spraynom1.asc

open

Step 2 looking at the time series plot to see the trends of the samples in each variable if they are stable or not stable and the scatter plots to see the patterns of the sample in bivariate variables either they are correlated or not.

Click on view

Time Series Plot

Then scroll on the variables to see the time series plot of each

Click on view

Scatter Plot

Then scroll on the variables to see the bivariate scatter plots of the variables.

Step 3 analyses of the data using PCA to identify possible relationship, outlier etc.

Click on analysis

Click on PCA

Select the appropriate number of principal component i.e. overwrite number in 'number of PC's and press return'

Check the univariate score plot of the PC1 and PC2 check for outlier and the numbers of outlier to determine if the process is under control or not

Then check the bivariate score plot between the two PC,s to check the relationship and find out if there are outliers or not

Use differential contribution plot to check what variables are contributing to the outlier and their magnitude in contribution

Use the residual contribution plot to investigate the contribution of individual variables to the squared prediction error for single observation and also investigate the specific values of the contribution of the current point and the preceding time points.

Analyse the T2 plot and score plot

Finally build the model for monitoring the spray time process.

II

Fig 1 scatter plots of variables

From fig 1 it can been seen clearly that there exist no pattern between all the variables which means there is high variability in the process variables which indicate that larger number of principal component needed to be retain to cover the information needed on the monitoring of the drying process.

The process variables measured are;

1 RELATIVE HUMIDIDY OF INLET AIR

2 ATMOSPHERIC AIR TEMPRATURE

3 TOTAL VAPOUR PRESSURE

4 INLET GAS TEMPRATURE

5 FEED LATEX DENSITY

6 INLET LATEX FLOW

7 INLET LATEX TEMPRATURE

8 LATEX PRESSURE

9 SPRAYING AIR FLOW

10 SPRAYING AIR PRESSURE

11 SPRAY DRYER DEPRESSION

12 RELATIVE HUMIDITY OF OUTLET

13 OUTLET GAS TEMPRATURE

14 DRYING GAS FLOW

15 FAN S714 INTENSITY

Fig 2 time series plot of variable 4

From fig 2 it can been seen clearly that that the distribution of sample in variable 4 is not stable showing the instability of the samples in variable 4

NORMINAL REPRESENTATION

Fig3 Bivarate score plot of PC 2 against PC 1

From fig 2 it can been seen that some samples are out of the action limit in both PC1 and PC2,this clearly shows the limitation of univariate score plot of PC1(fig4) and PC2(fig5) which shows no samples outside the action limit(outlier)

Fig 4 Univariate score plot of PC1

Fig 5 Univariate score plot of PC2

Fig6 Bivariate score plot of PC 2 against PC 1 showing nominal samples (blue that are within specification limit), first cluster (green) and second cluster (pink) colour that are out of specification(outlier)

Fig 7 Contribution plot for the green outlier in fig 6

Fig 7 above shows the contribution plot of the green colour marked outlier in fig 6,it can be deduce from fig 7 above that variable 6,8,11,14 and 15 are the major contributor to the the green outlier in pc1 and the most contributor is inlet latex flow variable 6.

Fig 8 Contribution plot for the green outlier in fig 6

Fig 8 above shows the contribution plot of the green colour marked outlier in fig 6,it can be deduce from fig 8 above that variable 1,10 and 15 are the major contributor to the the green outlier in PC2 and the most contributor is the spraying air pressure variable 10.

From the contribution plot of fig 7 it is observed that the major contributor of the green outlier(fig6) is variable 6 in PC1 which is having little contribution in PC2,this is one of the advantages of Bivariate score plot .

Fig 9 Contribution plot for the pink outlier in fig 6

Fig 9 above shows the contribution plot of the pink colour marked outlier in fig 6,it can be deduce from fig 9 above that variable 6,7,8,11,14 and 15 are the major contributor to the the pink outlier in pc1 and the most contributor is inlet latex flow variable 6.

Fig 10 Contribution plot for the pink outlier in fig 6

Fig 10 above shows the contribution plot of the pink colour marked outlier in fig 6,it can be deduce from fig 10 above that variable 1,2,10 and 14 are the major contributor to the the pink outlier in PC2 and the most contributor is the inlet latex temprature variable 7.

From the contribution plot of fig 9 it is observed that the major contributor of the pink outlier in PC 1(fig6) is variable 6 which is also the major contributor for the green outlier in PC1 and it is making a little contribution for both the green and pink outlier (fig6) in PC2.

Remember to put the SPE and hotelling T2 plot hear.

Fig 13 Univariate score plot of PC3

The univariate plot of PC3 is showing that no samples found outside the specification limit implying that the monitoring process is under control but to really know what is happening the Bivariate score plot will tell us better.

Fig 14 Bivariate score plot of PC 4 against PC 3 showing nominal samples (blue) that are within specification limit), first cluster (red) and second cluster (green) colour that are out of specification(outlier)

Fig 15 Contribution plot for the red outlier in fig 14

Fig 15 above shows the contribution plot of the red colour marked outlier in fig 14,it can be deduce from fig 15 above that variable 8,13, and 14 are the major contributor to the the green outlier in PC3 and the most contributor is outlet gas temprature, variable 6.

Fig 16 Contribution plot for the red outlier in fig 14

Fig 16 above shows the contribution plot of the red colour marked outlier in fig 14,it can be deduce from fig 16 above that variable 8,12,13, and 14 are the major contributor to the the green outlier in PC4 and the most contributor is outlet gas temprature, variable 13

Remain two diagram here.

Fig 18 SPE plot for 8PC(s)

Fig 19 Hotelling plot for 8PC(s)

Fig 20 Bivariate score plot of PC 5 against PC 6 showing nominal samples (blue) that are within specification limit), first cluster (red) and second cluster (green) colour that are out of specification(outlier)

Fig 21 Contribution plot for the red outlier in fig 14

Fig 21 above shows the contribution plot of the red colour marked outlier in fig 20,it can be deduce from fig 16 above that variable 9,12, and 13 are the major contributor to the the green outlier in PC5 and the most contributor is spraying air flow, variable 9.

Fig 22 Contribution plot for the red outlier in fig 14

Fig 22 above shows the contribution plot of the red colour marked outlier in fig 20,it can be deduce from fig 16 above that variable 12 and 13 are the major contributor to the the green outlier in PC6 and the most contributor is outlet gas temprature, variable 13

Fig 23 Contribution plot for the red outlier in fig 14

Fig 23 above shows the contribution plot of the red colour marked outlier in fig 20,it can be deduce from fig 23 above that variable 5,9, and 11 are the major contributor to the the green outlier in PC5 and the most contributor is spraying air flow, variable 9.

Fig 24 Contribution plot for the red outlier in fig 14

Fig 24 above shows the contribution plot of the red colour marked outlier in fig20 ,it can be deduce from fig 16 above that variable 3,8 and 11 are the major contributor to the the green outlier in PC6 and the most contributor is latex pressure, variable 8

Fig 25 Contribution plot for the red outlier in fig 14

Fig 25 above shows the contribution plot of the red colour marked outlier in fig 20,it can be deduce from fig 25 above that variable 9 and 13 are the major contributor to the the green outlier in PC5 and the most contributor is outlet gas temprature, variable 13

Fig 26 Contribution plot for the red outlier in fig 14

Fig 26 above shows the contribution plot of the red colour marked outlier in fig 20,it can be deduce from fig 26 above that variable 12 and 13 are the major contributor to the the green outlier in PC6 and the most contributor is outlet gas temprature, variable 13

Fig 27 SPE plot for 8PC(s)

Fig 28 Hotelling T2 plot for 8PC(s)

Fig29 Univariate score plot of PC5

Fig 30 Univariate score plot of PC6

Fig 31 Bivariate score plot of PC 7 against PC 8 showing nominal samples (blue) that are within specification limit), first cluster (red) and second cluster (green) colour that are out of specification(outlier)

Fig 32 Contribution plot for the red outlier in fig 31

Fig 32 above shows the contribution plot of the red colour marked outlier sample 90 in fig 31,it can be deduce from fig 32 above that variable 9 and 10 are the major contributor to the the red outlier in PC 7 and the most contributor to the sample 90 is spraying air flow, variable 9

Fig 33

Fig 34 Contribution plot for the red outlier in fig 31

Fig 34 above shows the contribution plot of the red colour marked outlier in fig 31,it can be deduce from fig 34 above that variable 4 and 7 are the major contributor to the the green outlier in PC7 and the most contributor is inlet latex temprature, variable 7

Fig 35 Contribution plot for the red outlier in fig 31

Fig 35 above shows the contribution plot of the red colour marked outlier in fig 31,it can be deduce from fig 35 above that variable 9(spraying air flow )is the only major contributor to the outlier.

Fig 36 Contribution plot for the red outlier in fig 31

Fig 36 above shows the contribution plot of the red colour marked outlier in fig 31,it can be deduce from fig 36 above that variable 2 and 9 are the major contributor to the the green outlier in PC8 and the most contributor is atmospheric air temprature temprature, variable 2

Fig 37

Fig 38 Univariate score plot of PC7

Fig 39 Univariate score plot of PC8

Fig 40 SPE plot for 8PC(s)

Fig41 Hotelling plot for 8PC(s)

III EXPEREMENTAL REPRESENTATION

Fig 42 Bivariate plot of PC8 against PC7 for nominal and experimental samples.

Fig 43 Contribution plot for the red outlier in fig 42

Fig 43 above shows the contribution plot of the red colour marked outlier in fig 42,it can be deduce from fig 43 above that variable 9,10 and 11 are the major contributor to the the green outlier in PC7 and the most contributor is spraying air pressure, variable10 also it can be deduce from fig 43 above that variable 2 and 8 are the major contributor to the the green outlier in PC7 and the most contributor is atmospheric air temprature, variable 2

Fig 44 Contribution plot for the red outlier in fig 42

Fig 44 above shows the contribution plot of the brown colour marked outlier in fig 42,it can be deduce from fig 44 above that variable 2,7 and 11 are the major contributor to the the green outlier in PC7 and the most contributor is spraying air flow, variable9 also it can be deduce from fig 44 above that variable 2 and 7 are the major contributor to the the green outlier in PC8 and the most contributor is inlet latex temprature, variable 7

Fig 45 Contribution plot for the red outlier in fig 42

Fig 45 above shows the contribution plot of the black colour marked outlier in fig 42,it can be deduce from fig 45 above that variable 3 and 10 are the major contributor to the the green outlier in PC7 and the most contributor is spraying air pressure, variable10 also it can be deduce from fig 45 above that variable 2 and 5 are the major contributor to the the green outlier in PC8 and the most contributor is feed latex density, variable 5

Fig 46 Contribution plot for the red outlier in fig 42

Fig 46 above shows the contribution plot of thelight blue colour marked outlier in fig 42,it can be deduce from fig 46 above that variable 2 and 10 are the major contributor to the the green outlier in PC7 and the most contributor is atmospheric air temprature, variable2 also it can be deduce from fig 46 above that variable 2 and 5 are the major contributor to the the green outlier in PC8 and the most contributor is atmospheric air temprature, variable 2

Fig 47 Contribution plot for the red outlier in fig 42

Fig 47 above shows the contribution plot of the light brown colour marked outlier in fig 42,it can be deduce from fig 47 above that variable 9 and 10 are the major contributor to the the green outlier in PC7 and the most contributor is spraying air pressure, variable10 also it can be deduce from fig 47 above that variable 5,7 and 14 are the major contributor to the the green outlier in PC8 and the most contributor is feed latex density, variable 5

Fig 48 Univariate score plot of PC8

From the univariate plot of PC 8 in fig 48 above it can be seen that the process is not under statistic control since many ouliers are found

Fig 49 SPE plot and Hotelling plot for 8PC(s)

The hotelling plot and the T2 plot above shows that the norminal process is under control while the experimental is out of statistical control .

Conclusion

From the nominal analysis it is seen from the univariate(fig 38 and 39), bivariate(fig 31) score plot that the drying process is under control 3 outliers out of 502 variables which means that the process is under control but using the model on the experimental a lot of outliers was found(fig 42) implying that the system is not under control confirming that the model procedure for the nominal data is not the best fit for the experimental data.

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