Effectiveness of phase I applications for identifying randomly scattered out‐of‐control observations and estimating control chart parameters |
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| Authors: | Murat Caner Testik Christian H Weiß Yesim Koca Ozlem Muge Testik |
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| Affiliation: | 1. Industrial Engineering, Hacettepe University, Ankara, Beytepe, Turkey;2. Department of Mathematics and Statistics, Helmut Schmidt University Hamburg, Hamburg, Germany |
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| Abstract: | Estimation of unknown process parameters with fixed‐size samples are studied in the following. The standard textbook approach for phase I control chart implementation with a Shewhart control chart is evaluated for the case of normally distributed independent observations with random sampling. The  charts are simultaneously implemented by generating observations that have a given percentage of randomly scattered out‐of‐control observations. Simulating the phase I steps, where out‐of‐control samples are detected iteratively by determining trial control limits, identifying samples exceeding these limits, and revising the control limits, the standard practice is evaluated in terms of both detection performance and quality of parameter estimates. It is shown that standard phase I control chart implementations with 3‐σ‐limits may perform very poorly in identifying true out‐of‐control observations and providing a reference set of in‐control observations for estimation in some practical settings. A chart design with 2‐σ‐limits is recommended for a successful phase I analysis. |
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| Keywords: | control limit width estimation error phase I phase II performance Shewhart control chart statistical process control |
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charts are simultaneously implemented by generating observations that have a given percentage of randomly scattered out‐of‐control observations. Simulating the phase I steps, where out‐of‐control samples are detected iteratively by determining trial control limits, identifying samples exceeding these limits, and revising the control limits, the standard practice is evaluated in terms of both detection performance and quality of parameter estimates. It is shown that standard phase I control chart implementations with 3‐σ‐limits may perform very poorly in identifying true out‐of‐control observations and providing a reference set of in‐control observations for estimation in some practical settings. A chart design with 2‐σ‐limits is recommended for a successful phase I analysis.