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Related Concept Videos

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 Charts01:13

Interpreting X̄ Charts

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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.
An x̄ chart plots the values of individual measurements over time against control limits calculated from historical data. The central line...
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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.
An R chart plots the range of subsets of measurements collected from a process. Each point on the chart represents the range—defined as the difference between the maximum and minimum...
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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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Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Run charts, essentially line graphs plotted over time, serve as fundamental yet effective tools for process analysis. They chronicle data sequentially, facilitating the identification of trends, shifts, or cyclical movements. This graphical representation is instrumental in determining whether a process is stable or exhibits signs of potential instability indicative of special cause variation. In the healthcare domain, run charts depict infection rates over time, enabling hospitals to monitor...
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Related Experiment Video

Updated: Jan 8, 2026

Visualization of Low-Level Gamma Radiation Sources Using a Low-Cost, High-Sensitivity, Omnidirectional Compton Camera
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Considering AEWMA control chart applied to Gamma-distributed data with fixed and variable sampling intervals.

Shin-Li Lu1, Meng-Chiao Chen2, Jen-Hsiang Chen3

  • 1Department of Industrial and Systems Engineering, Chung Yuan Christian University, Taoyuan, Taiwan. shinlilu@cycu.edu.tw.

Scientific Reports
|December 12, 2025
PubMed
Summary
This summary is machine-generated.

The adaptive EWMA (AEWMA) control chart improves process monitoring for skewed data. Its variable sampling interval (VSI) scheme shows superior sensitivity and stability in detecting small process shifts compared to other methods.

Keywords:
Adaptive EWMA control chartAverage time-to-signalGamma distributionVariable sampling interval

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Area of Science:

  • Industrial Engineering
  • Statistical Process Control
  • Quality Management

Background:

  • Shewhart control charts are limited in detecting small process shifts.
  • Exponentially weighted moving average (EWMA) charts detect minor shifts but are slow to react to sudden changes.
  • Adaptive EWMA (AEWMA) control charts offer dynamic adjustments for enhanced monitoring.

Purpose of the Study:

  • To evaluate the performance of the adaptive EWMA (AEWMA) control chart for skewed data, specifically Gamma distributions.
  • To compare the effectiveness of fixed sampling interval (FSI) and variable sampling interval (VSI) schemes within the AEWMA framework.
  • To assess the sensitivity and stability of AEWMA charts in detecting small process shifts.

Main Methods:

  • Applied the Wilson-Hilferty transformation for normality approximation of skewed data.
  • Utilized Monte Carlo simulations to design and evaluate AEWMA FSI and VSI schemes.
  • Employed Average Time-to-Signal (ATS) as a performance metric, alongside Average Run Length (ARL).

Main Results:

  • The AEWMA VSI chart demonstrated higher sensitivity and stability in detecting small process shifts.
  • AEWMA charts showed improved performance over traditional EWMA charts for skewed data.
  • Variable sampling interval schemes generally outperformed fixed sampling interval schemes.

Conclusions:

  • The AEWMA VSI control chart is a robust and sensitive tool for monitoring processes with skewed data, particularly in industries like semiconductor manufacturing.
  • The study highlights the advantages of adaptive and variable sampling strategies in statistical process control.
  • AEWMA charts provide a valuable enhancement for quality management systems dealing with non-normally distributed process data.