The preparation of one batch of molten metal is called as heat. The factors of this situation may be Heat, Types of Castings, Time of Heating, etc. The response variables may be the number of defects on the surface of the castings, tonnages of castings produced, etc. In this case, if the number of response variables is only one, that is the number of defects on the surface of the castings or the tonnages of castings produced, then ANOVA can be used to analyze the data. Since, we need to consider more than one response variables simultaneously, an improved analysis is warranted. The technique like Grey Relational analysis can be used to draw conclusion for problems with more than one response variable. But, it is only an approximation approach using orthogonal design. The exact and detailed analysis of this situation can be done using multivariate analysis of variance (MANOVA) since it uses the variance-covariance between variables in testing the statistical significance of the mean differences.
MANOVA is based on the product of model variance matrix as it can minimize the optimal issues facing the corporate nowadays. As an example, consider the foundry of a company manufacturing castings. The process of castings has the stages of preparing the molten metal using a furnace, tapping the molten metal in ladle and shifting the ladle to the casting area for pouring the molten metal into the mould of the casting.