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The X̄ Chart00:58

The X̄ Chart

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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.
A x̄ chart is constructed by plotting individual measurements of a quality...
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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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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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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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The R Chart01:02

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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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Run Charts01:12

Run Charts

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Run charts serve as an essential instrument for visualizing the performance of various processes over time, enabling the identification of trends and patterns crucial for quality improvement. These charts map out a series of data points chronologically, offering insights into the stability and efficiency of a process. A run chart's creation involves plotting data points on a graph, with the time intervals on the horizontal axis and the specific measurements on the vertical axis. For...
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  11. Variable Sample Size Based Ewma Control Chart With An Exponential Scaling Mechanism For Production Process Monitoring.

Variable sample size based EWMA control chart with an exponential scaling mechanism for production process monitoring.

Ibrahim A Nafisah1, Mohammed M A Almazah2, A Y Al-Rezami3

  • 1Department of Statistics and Operations Research, College of Sciences, King Saud University, P. O. Box 2454, 11451, Riyadh, Saudi Arabia.

Scientific Reports
|August 22, 2025

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View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces an adaptive sample size EWMA control chart for enhanced statistical process control. The new chart effectively detects process variations, outperforming existing methods in detecting small to moderate shifts.

Area of Science:

  • Industrial Engineering
  • Statistical Quality Control
  • Operations Research

Background:

  • Statistical Process Control (SPC) is crucial for maintaining stable production processes.
  • Detecting process variations is key to preventing defects and ensuring quality.
  • Existing EWMA charts have limitations in adapting to changing process variations.

Purpose of the Study:

  • To develop and evaluate a novel EWMA control chart with an adaptive sample size.
  • To improve the sensitivity and efficiency of shift detection in SPC.
  • To provide a robust tool for real-world process monitoring.

Main Methods:

  • Development of an Exponentially Weighted Moving Average (EWMA) control chart with adaptive sample sizing.
  • Performance evaluation using extensive Monte Carlo simulations.
Keywords:
Adaptive control chartAverage run lengthControl chartSPC

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  • Comparison with Fixed Sample Size EWMA (FEWMA) and Variable Sample Size EWMA charts.
  • Analysis of a real-world industrial dataset.

    • Main Results:

    • The proposed adaptive sample size EWMA chart demonstrates superior performance in shift detection compared to FEWMA and Variable Sample Size EWMA charts.
    • The chart is particularly effective in identifying small to moderate process shifts.
    • Metrics like Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) confirm enhanced detection capabilities.
    • The method balances detection sensitivity with computational efficiency.

    Conclusions:

    • The adaptive sample size EWMA chart offers a significant advancement in Statistical Process Control.
    • This method provides a more responsive and robust approach to monitoring process variations.
    • Its practical applicability is validated through real-world data analysis, highlighting its value in industrial settings.
    Variable sample size