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While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
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The X̄ Chart00:58

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The  x̄ chart is a statistical tool for monitoring the means in a process.
The x̄ chart, often known as the individual control chart, is a crucial tool in statistical process control. It is designed to monitor process behavior and performance over time and is widely used in various industries to ensure that processes are operating at their optimum capacity and within specified limits.
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Interpreting X̄ Charts01:13

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Interpreting x̄ charts, a type of control chart used in statistical process control helps monitor the variation in processes over time. The x̄ chart is based on the sample mean and allows for monitoring variations in the process mean over time. These charts are pivotal for quality assurance in manufacturing and other sectors.
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The R Chart01:02

The R Chart

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In statistical process control, control charts, particularly R charts, are instrumental in monitoring process variations and identifying non-random patterns that run charts might miss. R charts track the variability within process subgroups, which is crucial when standard deviation use is impractical or unknown process variations exist.
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Introduction to Statistical Process Control01:15

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Statistical Process Control (SPC) is a method used to monitor and control quality within processes, particularly in manufacturing and service delivery, by employing statistical methods. SPC aims to distinguish between natural (common cause) variation and variation due to specific changes or events (special cause), allowing for timely improvements and sustained quality. The control chart, a pivotal tool in SPC, visually displays data over time alongside a central line of upper and lower control...
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Interpreting R Charts01:22

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R chart, or range chart, is a fundamental tool in statistical process control used to monitor the variability within a process. It complements the X-bar (x̄) chart by focusing on the range of the data, rather than individual values, providing a clear picture of the process dispersion over time.
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Updated: May 28, 2025

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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.

Journal of Applied Statistics
|February 14, 2025
PubMed
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.