Historical data analysis based on plots of independent and parallel coordinates and statistical control limits

Interactive multidimensional visualisation based on parallel coordinates has been studied previously as a tool for process historical data analysis. Here attention is given to improvement of the technique by the introduction of dimension reduction and upper and lower limits for separating abnormal data to the plots of coordinates. Dimension reduction using independent component analysis transforms the original variables to a smaller number of latent variables which are statistically independent to each other. This enables the visualisation technique to handle a large number of variables more effectively, particularly when the original variables have recycling and interacting correlations and dependencies. Statistical independence between the parallel coordinates also makes it possible to calculate upper and lower limits (UL and LL) for each coordinate separating abnormal data from normal. Calculation of the UL and LL limits requires each coordinate to satisfy Gaussian distribution. In this work a method called the Box–Cox transformation is proposed to transform the non-Gaussian coordinate to a Gaussian distribution before the UL and LL limits are calculated.