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Memory type Bayesian adaptive max-EWMA control chart for weibull processes.

Abdullah A Zaagan1, Imad Khan2, Amel Ayari-Akkari3

  • 1Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, 45142, Jazan, Saudi Arabia.

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|April 18, 2024
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Summary

This study introduces a new Bayesian adaptive maximum exponentially weighted moving average (Max-EWMA) control chart for monitoring non-normal processes. The proposed chart effectively detects process shifts, outperforming existing methods in semiconductor manufacturing.

Keywords:
Average run lengthBayesian approachControl chartInverse response functionMax-EWMAThe Weibull process

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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 normal distributions.
  • Existing methods often assume normality, limiting their application to non-normal processes.
  • Effective monitoring of non-normal processes requires specialized control charting techniques.

Purpose of the Study:

  • To introduce a novel Bayesian adaptive maximum exponentially weighted moving average (Max-EWMA) control chart.
  • To jointly monitor the mean and dispersion of non-normal processes, specifically those following a Weibull distribution.
  • To evaluate the proposed chart's performance against existing Max-EWMA charts.

Main Methods:

  • Utilized the inverse response function for Weibull distributed processes.
  • Employed Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) for performance assessment.
  • Compared the proposed Bayesian Max-EWMA chart with a traditional Max-EWMA chart.

Main Results:

  • The proposed Bayesian Max-EWMA control chart demonstrated superior sensitivity in detecting out-of-control signals.
  • The chart showed effective performance for Weibull processes under various Loss Functions (LFs).
  • A case study on the semiconductor hard-bake process validated the chart's practical applicability and rapid detection capabilities.

Conclusions:

  • The novel Bayesian adaptive Max-EWMA control chart is highly effective for monitoring non-normal processes.
  • The proposed chart offers significant improvements in detecting process deviations compared to existing methods.
  • This contributes to enhanced process monitoring and quality control in industries like semiconductor manufacturing.