Generalized contribution plots in multivariate statistical process monitoring

This paper discusses contribution plots for both the D-statistic and the Q-statistic in multivariate statistical process control of batch processes. Contributions of process variables to the D-statistic are generalized to any type of latent variable model with or without orthogonality constraints. The calculation of contributions to the Q-statistic is discussed. Control limits for both types of contributions are introduced to show the relative importance of a contribution compared to the contributions of the corresponding process variables in the batches obtained under normal operating conditions. The contributions are introduced for off-line monitoring of batch processes, but can easily be extended to on-line monitoring and to continuous processes, as is shown in this paper.