The effect of parameter estimation on the performance of one-sided Shewhart control charts for zero-inflated processes |
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Authors: | Athanasios C Rakitzis Philippe Castagliola |
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Institution: | 1. Department of Mathematics, University of Aegean, Karlovasi, Samos, Greecearakitz@aegean.gr;3. LUNAM Université, Université de Nantes &4. IRCCyN UMR CNRS 6597, Nantes, France |
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Abstract: | ABSTRACTZero-inflated probability models are used to model count data that have an excessive number of zeros. Shewhart-type control charts have been proposed for the monitoring of zero-inflated processes. Usually their performance is evaluated under the assumption of known process parameters. However, in practice, their values are rarely known and they have to be estimated from an in-control historical Phase I sample. In the present paper, we investigate the performance of Shewhart-type control charts for zero-inflated processes with estimated parameters and propose practical guidelines for the statistical design of the examined charts, when the size of the preliminary sample is predetermined. |
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Keywords: | Average run length Estimated parameters Moment estimator One-sided Shewhart control charts Probability generating function Standard deviation run length Zero-inflated Binomial distribution Zero-inflated Poisson distribution |
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