ISBIS4 Abstract

Contact Author's Name: Balgobin Nandram
Title of Abstract: A Bayesian Predictive Inference for Multivariate Control Charting
Author(s): Balgobin Nandram, Brenda Ramirej, Jai Won Choi
Affiliation: Worcester Polytechnic Institute


Statistical process control has been applied with marginal success in the semiconductor
industry. This may be, in part, due to a heavy reliance on univariate control chart practices
when the quality of many production processes is characterized by a number of variables
which may be highly correlated. When the data are correlated, the univariate charts are
not as sensitive to out-of-control values as the multivariate charts which incorporate the
correlation. It is, therefore, pertinent to use multivariate control charts to perform statistical
process monitoring for such processes. Multivariate control charts can be used eectively
to monitor the quality of complex processes with several critical variables simultaneously.
However, when the covariance matrix has large dimensions in comparison to the number of
runs available for parameter estimation, these charts can perform poorly. We incorporate
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prior information about the covariance matrix in which the number of parameters is reduced
to just two. There are many semiconductor manufacturing processes that may induce a
covariance structure that conforms to the parsimonious covariance that we are proposing
(correlation that degrades with distance). Two examples are an LPCVD (low pressure
chemical vapor deposition) reactor that is used for the deposition of polysilicon or nitride,
and PECVD (plasma enhanced chemical vapor deposition) of nitride or oxide. We consider a
passivation process for semiconductor manufacturing, where each of the variables represents
a value at a specic location in a passivation tube, and because of the interaction between
the plasma and the reactant gases owing 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 T2, is
used for charting. The control limits are constructed using a Bayesian predictive inference,
and the Metropolis-Hastings algorithm is used to perform the computations. Simulations
show that our method can detect out-of-control observations more quickly than the classical
multivariate approach. Also our method is robust against departures from the parsimonious
covariance structure.
KEY WORDS: Average run length; Correlation; Hotelling's T2; Metropolis-Hastings
algorithm; Semiconductor data; Screening and monitoring.
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