Analysis of Historical Data
-how to improve control of a complex process.
Experience and production data had revealed several steps in the process with large and uncontrolled variation. This was clear from the large differences in the quantities of produced metal. Examples were qualities of manufacturing and drying of pellets.
The purpose of the investigation was to quantify the relations between production quantities and feed/ process data, first to see if the measured data contained enough information to model the variation in the production quantities, next to use the analysis as an example of a general strategy to extract and evaluate information from historical data
The data table shows the average measurements in 26 weeks.
The variables are:
The figure below shows how the amount of produced metal varies.
The data had been analysed earlier by use of multiple linear regression (MLR) and stepwise MLR. MLR assumes implicitly that all predictor variables are free of error and that all errors are located to the response variables. It is more likely that the produced quantities are measured with small errors and that the other variables contain larger errors. A better method is to relate the quantities to the predictors by a principal component analysis (PCA). PCA has not this restriction, and in addition, PCA takes care of correlations among the variables.
The PCA with standardised variables gave 3 PC`s that accounted for 87.8% of the variation in the data.
From the Biplot between PC1 vs. PC2:
It is seen that Cryst and Pore-1 are anti-correlated to each other and un-correlated to produced quantity (the angle is about 90 degrees to the line from origin to Amount). Stop is placed in origin and has no correlation with the others.
Using Sirius, a PLS model between the produced quantities and the other variables was then established. This PLS model accounted for 63.7% of variation in quantity, and it was evident that important variables were missing in the data.
During stops in the pellets production, stored pellets was used to maintain the production. In these situations the production decreased. Since it was impossible to provide any direct measure of «pellets quality», the discharge of SO2 was used as an indirect indicator of pellets quality. When the pellets quality decreases, the discharge of SO2 increases. Thus this variable (SO2) was incorporated in the response model, with profound effect.
The improved model gave 2 significant PLS components that accounted for 75.7% of the variation in the produced quantities of metal.
The Biplot shows that SO2 (pellets quality) is anti-correlated with Amount, that is, high SO2 (bad pellets quality) indicates decrease in the production. Discharges (SO2) is negatively correlated with optimal yield of production. This is an ideal, but fortunately usual connection in industrial processes.
The plot of the predicted vs the measured metal yield, shows good predictions for all weeks, except week 24. The Normal plot of response residuals confirms that this is a good model.
The analysis revealed that quality in raw materials and pellets was of vital importance for the produced quantities of metal. It was consequently crucial to find a method for the analysis that could characterise the pellets quality with variables that could be used to control and to optimise the pellets production.
In this particular step in the process, the annual earning potential summed up to $ 4 mill.
THIS EXAMPLE SHOWS THAT A MULTIVARIATE STRATEGY USING SIRIUS FOR PROCESS OPTIMISATION GIVES KNOWLEDGE WHICH IS NOT AVAILABLE FROM STANDARD UNIVARIATE STATISTICAL TECHNIQUES.
THE NEED FOR CHEMOMETRICS IS PROBABLY MOST EVIDENT IN RELATING THE (PRINCIPAL) QUALITIES OF THE END PRODUCT TO THE CHARACTERISTICS OF THE FEED (THE INPUT MATERIALS) AND THE RUNNING AND MONITORING OF THE MANUFACTURING PROCESS. (THE TERM PRINCIPAL QUALITIES IS USED TO SIGNIFY A COMBINATION OF SINGLE QUALITY MEASURES INTO ONE OR MORE LATENT VARIABLES).
LATENT-VARIABLE ANALYSIS REPRESENTS A POWERFUL TOOL FOR THE ANALYSIS OF COMPLEX SYSTEMS TO ENSURE THE OPTIMAL PROPERTIES OF A PRODUCT IN THE LIGHT OF DEVELOPMENT, MANUFACTURING, ENVIRONMENTAL DEMANDS, MARKETING AND DISTRIBUTION COSTS.