The complex data characteristics collected in Industry 4.0 cannot be efficiently handled by classical Six Sigma statistical toolkit based mainly in least squares techniques. This may refrain people from using Six Sigma in these contexts. The incorporation of latent variables-based multivariate statistical techniques such as principal component analysis and partial least squares into the Six Sigma statistical toolkit can help to overcome this problem yielding the Multivariate Six Sigma: a powerful process improvement methodology for Industry 4.0. A multivariate Six Sigma case study based on the batch production of one of the star products at a chemical plant is presented.