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A partitioned weighted moving average control chart.

Raja Fawad Zafar1,2, Michael B C Khoo1, Huay Woon You3

  • 1School of Mathematical Sciences, Universiti Sains Malaysia, Minden, Malaysia.

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|February 14, 2025
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Summary
This summary is machine-generated.

The new partitioned weighted moving average (PWMA) chart offers superior performance over EWMA and HWMA charts for detecting process shifts. Its effectiveness increases with partitioning time, demonstrating robustness in statistical process control.

Keywords:
Partitioned weighted moving average (PWMA)exponentially weighted moving average (EWMA)homogenously weighted moving average (HWMA)steady statezero state

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Area of Science:

  • Statistical Process Control
  • Quality Engineering
  • Industrial Statistics

Background:

  • Traditional control charts like EWMA and HWMA have limitations in detecting subtle process variations.
  • Effective statistical process control requires methods sensitive to small shifts and robust to parameter estimation.

Purpose of the Study:

  • To introduce and evaluate the performance of a novel Partitioned Weighted Moving Average (PWMA) control chart.
  • To compare the PWMA chart against EWMA and HWMA charts under various conditions, including different shift sizes and smoothing constants.

Main Methods:

  • Development of the PWMA chart by partitioning samples into two groups and calculating weighted averages.
  • Comparative analysis of PWMA, EWMA, and HWMA charts using simulation or theoretical evaluation for zero and steady-state conditions.
  • Assessment of chart performance based on shift detection capabilities for varying parameters (n, λ, δ, j).

Main Results:

  • The PWMA chart generally outperforms EWMA and HWMA charts, especially for detecting small process shifts (δ).
  • PWMA chart's superiority increases with the partitioning time period (j).
  • The PWMA chart shows robustness to non-normality and estimated process parameters, enhancing its practical applicability.

Conclusions:

  • The PWMA chart is a more effective tool for statistical process control compared to EWMA and HWMA charts.
  • Its design provides better control over weight distribution, leading to improved sensitivity in detecting process disturbances.
  • The PWMA chart's robustness makes it a valuable alternative for real-world quality management systems.