Lacotid (faked name) is a white crystalline powder used in medicine. The synthesis of Lacotid is a two stage process: 1) synthesis 2) crystallization. The synthesis of the raw products is performed in a methanol solution (MeOH). A slurry of the raw product is then pumped into a new container where crystallization takes place. Crystallization is performed by gradually adding isopropanol (C3H7OH) to the slurry. The producers of Lacotid wanted to increase the yield and make the production more optimal and stable, as there was a yield of only 50% and large variations in quality. After some initial experiments the factory concluded that the main variations occurred in the crystallization stage. They therefore planned to improve the monitoring of the crystallization process to ensure stable and optimal production of Lacotid with respect to yield and quality. To achieve this they first needed to find which process parameters have significant effects on the yield.
It was decided to study the crystallization process using a factorial experimental design to determine the main effects. Some parameters were assumed to have little or no effect on yield and quality, and were thus not investigated. In factorial designs all X-variables take only two values (high or low), because the goal is to investigate if Y is affected by a change in each X-variable. Because of problems in keeping some of the variables at their planned levels, the data couldn't be analyzed by the traditional methods used to analyze experimental designs. They therefore had to work with the real x-values and use a PLS model instead to interpret the variable relationships.
Explained variance as a function of the number of PLS-components.
The first component describes 75% of the variance of the Yield (the rest of Methanol at start and the proportion of Methanol in the solution), see figure above.
The loading plot suggests variable X1 and X2 as the most important for the Yield in the first PLS component. X6, the lowest crystallization temperature has some contribution in PC2.
The loading plot shows important variables and correlations
From the loading plot it is clear that variable X1 and X2 covary. We can't say if they also interact, unless we add the variable X1*X2 in the X-matrix. The high degree of explained Y-variance (80% at 2 PCs) without the interaction term suggests that this is not a significant effect.
X4 stirring speed, X5 feed velocity and X7 the duration of the temperature has little effect on the crystallization, and do not need to be better controlled.