Westerhuis et al. (J. Chemometrics 1998; 12: 301–321) show that the scores of consensus PCA and multiblock PLS (Westerhuis and Coenegracht, J. Chemometrics 1997; 11: 379–392) can be calculated directly from the regular PCA and PLS scores respectively. In this paper we show that both the loadings and scores of consensus PCA can be calculated directly from those of regular PCA, and the multiblock PLS loadings, weights and scores can be calculated directly from those of regular PLS. The orthogonal properties of four multiblock PCA and PLS algorithms are explored. The use of multiblock PCA and PLS for decentralized monitoring and diagnosis is derived in terms of regular PCA and PLS scores and residuals. While the multiblock analysis algorithms are basically equivalent to regular PCA and PLS, blocking of process variables in a large-scale plant based on process knowledge helps to localize the root cause of the fault in a decentralized manner. New definitions of block and variable contributions to SPE and T 2 are proposed for decentralized monitoring. This decentralized monitoring method based on proper variable blocking is successfully applied to an industrial polyester film process. Copyright © 2001 John Wiley & Sons, Ltd.