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c-charts, X-charts, and the Katz Family of Distributions

Summary: [This abstract is based on the author's abstract.] The c-chart is the principle method used to monitor the number of nonconformities in statistical process control. The conventional c-chart assumes that nonconformities in samples are well modeled by a Poisson distribution, but when that assumption is not met, the X-chart is often used as an alternative. The relative merits of the c-chart are compared to the X-chart for the Katz family of distributions relative to the Poisson distribution. Use of the X-chart can lead to significant improvements under certain circumstances, but both 3-sigma c- and X-charts fail to provide reliable information with a small in-control process mean when a downward mean shift occurs.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Average run length (ARL),Modified likelihood ratio principle,Poisson process,C chart (count chart),Statistical process control (SPC),X-bar charts,Robust design
  • Author: Fang, Yue
  • Journal: Journal of Quality Technology