Confidence limits for contribution plots

An issue often raised in multivariate statistical process control, when usi ng statistical projection-based techniques to define nominal process behavi our, is that of the assured identification of the variables causing an out- of-statistical-control signal. One approach which has been adopted is that once a change in process operating conditions has been detected, the contri bution of the individual variables to the principal component scores or squ ared prediction error, the Q-statistic, are examined. Adopting this approac h, it is important that those variables responsible for, or contributing to , the process change are clearly identifiable. In process modelling and est imation studies, confidence bounds are typically placed around the model pr edictions. Currently confidence bounds are not used to identify the limits of normal behaviour for the individual multivariate statistical contributio ns, resulting in the interpretation of the contribution plot being left to the user. This paper presents a potential solution to the definition of con fidence bounds for contribution plots. The methodology is based on bootstra p estimates of the standard deviations of the loading matrix. The proposed approach is evaluated using data from a benchmark simulation of a continuou s stirred tank reactor system. The preliminary results are encouraging. Cop yright (C) 2000 John Wiley & Sons, Ltd.