A Bayesian Control Chart for a Passivation Process

Multivariate control charts can be used effectively to monitor the quality of complex processes with several critical variables simultaneously. However, when the covariance matrix has large dimension in comparison to the number of runs available for parameter estimation, these charts can perform poorly. We incorporate prior information about the covariance matrix in which the number of parameters is reduced to just two. We consider a passivation process for semiconductor manufacturing, where each of the variables represents a value at a specific location in a passivation tube, and because of the interaction between the plasma and the reactant gases flowing down the tube, the correlation among the variables might decay with distance between these locations. Moreover, the variability at the locations might be taken equal, further reducing the number of parameters. We use a Bayesian method to construct the multivariate control chart, and a statistic, analogous to Hotelling's 2 T , is used for charting.