7Epsilon approach for data visualisation using penalty matrices


The data analysis and knowledge discovery stage of 7Epsilon project relies on visualising process data on influencing factors via penalty matrices. An example of the scatter diagram for %rejection due to shrinkage defect per batch for a nickel based alloy is shown in Figure 1.


  • The variability of the process response is analysed using scatter diagrams.
  • The first step in the data analysis stage is to identify regions of desired and undesired response variation. 
  • A zero penalty value is assigned to desired response and 100 penalty value is assigned to undesired response values. For intermediate values the penalty is scaled between zero and hundred. 
  • The novelty in the 7Epsilon approach is that the response penalty values are transferred onto factor scatter diagrams (Figure 3 left) and then  converted into penalty matrix format (Figure 3 right) in order to discover new knowledge after conducting a  confirmation trial .


A detailed discussion on this approach has been published in the Computers in Industry Journal.


Visit the YouTube Videos page to listen to presentations on constructing penalty matrices for main effects and interactions, and using the matrices to design a confirmation trial plan for single and multiple responses.