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Memory type Max-EWMA control chart for the Weibull process under the Bayesian theory.

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This study introduces a new Bayesian Max-EWMA control chart for simultaneously monitoring non-normal process mean and dispersion. The proposed chart demonstrates superior sensitivity in detecting process shifts compared to existing methods.

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Area of Science:

  • Statistical Process Control
  • Quality Engineering
  • Industrial Statistics

Background:

  • Simultaneous monitoring of process mean and dispersion is crucial, especially for non-normal processes.
  • Existing control charts often focus on normal distributions or individual parameters.
  • Effective monitoring is key to maintaining quality and efficiency in manufacturing.

Purpose of the Study:

  • To develop a novel Bayesian Max-EWMA control chart for simultaneous monitoring of non-normal process mean and dispersion.
  • To evaluate the performance of the proposed chart using Average Run Length (ARL) and Standard Deviation of Run Length (SDRL).
  • To compare the proposed chart's sensitivity against an existing Max-EWMA control chart.

Main Methods:

  • Utilized the inverse response function for Weibull distributed processes.
  • Employed Bayesian Max-EWMA methodology for simultaneous parameter tracking.
  • Assessed chart efficacy through ARL and SDRL metrics.
  • Conducted a comparative analysis with a standard Max-EWMA chart.

Main Results:

  • The proposed Bayesian Max-EWMA control chart shows higher sensitivity in detecting process variations.
  • Performance evaluation confirmed the chart's effectiveness in identifying out-of-control signals.
  • The chart demonstrated flexibility across different Loss Functions (LFs) for Weibull processes.

Conclusions:

  • The Bayesian Max-EWMA control chart offers a sensitive and effective tool for simultaneous process mean and dispersion monitoring.
  • The chart's application in semiconductor hard-bake processes highlights its practical utility.
  • Implementation of this chart can significantly enhance process monitoring and quality control in industrial settings.