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Posterior Control Chart for Process Average under Conjugate Prior Distribution

Posterior Control Chart for Process Average under Conjugate Prior Distribution Abstract Control charts for the process average play an important role in process control. In the presence of prior information, using Bayesian approach, one can construct posterior control chart for process average ( X ̅ posterior control chart). The control limits of the proposed chart are derived under the assumption that the process average has a conjugate prior distribution. Both cases – variance is known and variance is unknown – are discussed. When the variance is unknown, the control limits are constructed using Unbiased Estimator (UE) and Maximum Likelihood Estimator (MLE) of the variance. The power and Average Run Length (ARL) of the proposed chart are obtained. The newly constructed X ̅ posterior control chart is compared with a few other X ̅ charts described in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

Posterior Control Chart for Process Average under Conjugate Prior Distribution

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
0940-5151
eISSN
1869-6147
DOI
10.1515/eqc-2014-0003
Publisher site
See Article on Publisher Site

Abstract

Abstract Control charts for the process average play an important role in process control. In the presence of prior information, using Bayesian approach, one can construct posterior control chart for process average ( X ̅ posterior control chart). The control limits of the proposed chart are derived under the assumption that the process average has a conjugate prior distribution. Both cases – variance is known and variance is unknown – are discussed. When the variance is unknown, the control limits are constructed using Unbiased Estimator (UE) and Maximum Likelihood Estimator (MLE) of the variance. The power and Average Run Length (ARL) of the proposed chart are obtained. The newly constructed X ̅ posterior control chart is compared with a few other X ̅ charts described in the literature.

Journal

Economic Quality Controlde Gruyter

Published: Jun 1, 2014

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