Confidence limits for contribution plots
An issue often raised in multivariate statistical process control, when using statistical projection-based techniques to define nominal process behaviour, 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 contribution of the individual variables to the principal component scores or squared prediction error, the Q-statistic, are examined. Adopting this approach, it is important that those variables responsible for, or contributing to, the process change are clearly identifiable. In process modelling and estimation studies, confidence bounds are typically placed around the model predictions. Currently confidence bounds are not used to identify the limits of normal behaviour for the individual multivariate statistical contributions, resulting in the interpretation of the contribution plot being left to the user. This paper presents a potential solution to the definition of confidence bounds for contribution plots. The methodology is based on bootstrap estimates of the standard deviations of the loading matrix. The proposed approach is evaluated using data from a benchmark simulation of a continuous stirred tank reactor system. The preliminary results are encouraging. Copyright (C) 2000 John Wiley & Sons, Ltd.
confidence limits contribution plots principal component analysis