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Bayesian AEWMA control chart under ranked set sampling with application to reliability engineering.

Imad Khan1, Muhammad Noor-Ul-Amin2, Dost Muhammad Khan1

  • 1Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan.

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|November 17, 2023
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Summary
This summary is machine-generated.

This study introduces a new Bayesian AEWMA control chart using various loss functions and ranked set sampling (RSS) for improved process mean shift detection. The proposed chart demonstrates superior performance over existing methods, especially with RSS designs.

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Area of Science:

  • Statistical Process Control
  • Quality Engineering
  • Bayesian Inference

Background:

  • Traditional control charts struggle with detecting small process shifts.
  • Integrating diverse loss functions and sampling designs can enhance sensitivity.
  • Bayesian approaches offer a robust framework for uncertainty quantification.

Purpose of the Study:

  • To develop a novel Bayesian Exponentially Weighted Moving Average (AEWMA) control chart.
  • To incorporate multiple loss functions (e.g., square error, Linex) and ranked set sampling (RSS) designs.
  • To improve the detection of small to moderate shifts in the process mean.

Main Methods:

  • Implementation of a Bayesian AEWMA control chart with informative priors.
  • Utilization of various loss functions for posterior and posterior predictive distributions.
  • Application of diverse ranked set sampling (RSS) schemes and comparison with simple random sampling (SRS).
  • Performance evaluation using Average Run Length (ARL) and Standard Deviation of Run Length (SDRL).
  • Monte Carlo simulations and case study in semiconductor manufacturing (hard bake process).

Main Results:

  • The proposed Bayesian AEWMA control chart with integrated loss functions and RSS designs significantly outperforms existing charts.
  • Ranked set sampling (RSS) designs show superior performance in detecting process mean shifts compared to simple random sampling (SRS).
  • The chart effectively detects small to moderate shifts, demonstrating enhanced sensitivity in real-world applications.

Conclusions:

  • The developed Bayesian AEWMA control chart provides a more precise and efficient method for process mean shift detection.
  • Integrating multiple loss functions and RSS schemes enhances the chart's capability to identify out-of-control signals.
  • This approach offers a valuable tool for quality improvement in manufacturing processes.