With the complexity of most industrial processes and vast amount of data that can now be measured with modern analytics, it is difficult to predict a property using only one or two measured variables. Thus, we use a hybrid set of mathematical and statistical tools, like principal component analysis (PCA), to dissect all the data measured and find those pieces of relevant information that can be used to better characterize a system or process. PCA uses orthogonal transformation to convert a set of, possibly correlated variables, into a new set of uncorrelated variables called principal components (PCs). By transforming the X variables into uncorrelated variables, it becomes possible to use all of the data collected. Each principal component consists a set of scores and loadings vector. The scores are scalar quantities that pertain to the magnitude that each sample has on the overall variability in the data set. For example, a measurement that represents an extreme response would have a very large or perhaps very low score value relative to the other samples measured. The loading vector provides a fingerprint of the process and describes the measurement variables. The measurement variables that are most important will have a much greater weight in the loading vector compared to the variables that are consider insignificant or noise variables. By transforming the data into these new sets of data, the relevant information in a data set emerges. In addition, the data can be plotted in various ways thus providing an insightful visual representation of your process.
PCA forms the basis of many exploratory, classification, and quantitative algorithms that can transform all the data available in a way that is much easier to visualize relationships between the measured and dependent variables. The technique provides insightful information about systems and processes for making better decisions and future predictions. PCA can be used to decipher the vast amounts of data collected in manufacturing processes where multiple devices are used to collect data. The method is often applied in the fields of spectroscopy, chromatography, process scale-up, image analysis, and in many other disciplines.
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