A set of nominal operation condition (NOC) data, which includes the quality variables of interest and the related key process variables are generated from the developed dynamic simulation program. Selection of key process variables into the NOC data matrix is important to ensure that the variation of the two quality variables is exhibited in the selected key process variables. In this research, NOC is referred to situation the two quality variables of interest (oleic acid and linoleic acid composition in the bottom stream) and the selected key process variables (the key process variables that are shown in Table 4.2) are within the control limit of their control charts (Statistical Control Charts: Shewhart Control Chart and Range Control Chart).
During the generation of the NOC data, the selected key process variables from Table 4.2 (except Tbot) are fed with small random noise to make the two selected quality variables of interest from Table 4.1 to fluctuate within ± 5% of their SS value. The term noise in this research refers to measurement noise. The definition of noise was given in Section 2.2.4. The quality variables of interest and the selected key process variables are collected to form the NOC data matrix for the process variables, X and for the quality variables, Y. These NOC data matrices are represented in Equation 4.1 and Equation 4.2.
X = [F Tf Re P QR Tbot ] ( 4.1 )
Y = [X8 X9] ( 4.2 )
Where: F = data matrix for feed flow rate Tf = data matrix for feed temperature
Re = data matrix for reflux flow rate
P = data matrix for pumparound flow rate
QR = data matrix for reboiler duty Tbot = data matrix for bottom temperature
X8 = data matrix for oleic acid mole fraction in the bottom flow
X9 = data matrix for linoleic acid mole fraction in the bottom flow
4.2.3.1 Standardization of NOC Data
The data matrices of X and Y are standardized. The standardization procedure is for each of the variables in both data matrices. The standardization of each variable is shown as in Equation 4.3.
i i i i s x x z = − ( 4.3 )
Where: zi = standardized variable
xi = variable from measurements in X or Y xi = arithmetic average of variable xi
si = standard deviation of variable xi
The reason for standardization is that the measurements are consists of pressure, temperature, flow rates, compositions and other variables that have different scales and units of measurements. The standardization process will yield standardized variables with equivalent variance and mean centered. After this
85 procedure, both the data matrices are ready for further analysis in order to obtain NOC data.
4.2.3.2 Normality Test of NOC Data
In Multivariate Statistical Process Control (MSPC), the NOC data has to follow the normal distribution before any further manipulation of the NOC data can be carried out. The NOC data are subjected to normality test to study the normality properties of the NOC data. The normality tests on the NOC data include the checking of value of skewness, kurtosis, standard deviation and arithmetic average of the NOC data. For data following normal distribution, the skewness, kurtosis, standard deviation and arithmetic average of the data must have the value of 0, 3, 1 and 0, respectively (Wetherill and Brown, 1991). From the results of the normality test, the NOC data follow the normal distribution. Therefore, further manipulation of the NOC data can be carried out. The results of the normality tests of the NOC data are given in Section 5.4 of Chapter 5. Sometimes, the collected data are skewed and have a skewness value of more or less than 0. In this case, more data should be collected in order to get the data to have a skewness value of very near to 0. This method is based on Central Limit Theorem (CLT), which states that when enough data are collected in a data set, the data set will follow the normal distribution.
4.2.3.3 Number of Measurements in NOC Data
The number of measurements that has to be collected is the critical parameter. In this research, the range of the value of the two quality variables of interest for NOC data is set at 3σ where σ is the standard deviation of the quality variable. The reason for choosing this range value is in such a way that during NOC, 99.7% of points on the control chart for the quality variables are within the control limit for normally distributed data (McNeese and Klein, 1991). The method in obtaining the NOC data set is shown in Figure 4.1. The steps involving the analysis of the
standardized NOC data for correlation using Normal Correlation (NC), Principal Component Analysis (PCA) and Partial Correlation Analysis (PCorrA) and the building of control limits for the statistical control charts will be discussed in detail in Section 4.2.4.
Checking: Is 99.7% of data within the control limit? Standardization of NOC data. Analysis of data using NC, PCA and PCorrA. Building control limits for the statistical control charts.
Sampling NOC data (Process sampling time = TMSPC ) for both key process variables and quality variables of interest.
No
Yes NOC data is representable.
Figure 4.1: Procedure in obtaining the NOC data set
For 50 data points sampled with the process sampling time of 4.6 hours for each point sampled, all the data points of the quality variables and key process variables are within the control limits of their statistical control charts (more details of the statistical control charts are given in Section 4.2.5). Once the NOC data is obtained,
87 the correlation between the selected key process variables and the quality variables of interest will be determined.