Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes |
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Authors: | Chelsea L Jones Abdel-Salam G Abdel-Salam D'Arcy Mays |
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Affiliation: | 1. Department of Statistical Science and Operations Research, College of Humanities and Sciences, Virginia Commonwealth University, Richmond, Virginia, USA;2. Department of Mathematics, Statistics and Physics, Statistics Program, College of Arts and Sciences, Qatar University, Doha, Qatar |
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Abstract: | In this work, both the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been reconfigured to monitor processes using a Bayesian approach. Our construction of these charts are informed by posterior and posterior predictive distributions found using three loss functions: the squared error, precautionary, and linex. We use these control charts on count data, performing a simulation study to assess chart performance. Our simulations consist of sensitivity analysis of the out-of-control shift size and choice of hyper-parameters of the given distributions. Practical use of theses charts are evaluated on real data. |
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Keywords: | Bayesian EWMA loss functions Poisson conjugate statistical process control |
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