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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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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 R Charts01:22

Interpreting R Charts

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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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Introduction to Statistical Process Control01:15

Introduction to Statistical Process Control

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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

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.
R charts are pivotal for pinpointing shifts in process variability. Stability is indicated when all data points remain within the defined upper and lower...
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Random Error01:04

Random Error

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Updated: Jun 27, 2025

Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition
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Parameter free AEWMA control chart for dispersion in semiconductor manufacturing.

Abdullah A Zaagan1, Imad Khan2, Ali Rashash R Alzahrani3

  • 1Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, 45142, Jazan, Kingdom of Saudi Arabia.

Scientific Reports
|May 7, 2024
PubMed
Summary

A new parameter-free adaptive exponentially weighted moving average (AEWMA) control chart effectively monitors process dispersion shifts. This advanced chart demonstrates superior efficiency in detecting various dispersion changes compared to existing methods.

Keywords:
AEWMAAverage run lengthControl chartEWMAProcess dispersionStatistical process control

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Area of Science:

  • Industrial Engineering
  • Statistical Process Control

Background:

  • Process dispersion monitoring is crucial for quality control.
  • Existing methods may lack adaptability or efficiency in detecting shifts.

Purpose of the Study:

  • To introduce a novel parameter-free adaptive exponentially weighted moving average (AEWMA) control chart.
  • To enhance the detection of process dispersion shifts using an adaptive smoothing constant.

Main Methods:

  • Development of a parameter-free AEWMA control chart.
  • Utilizing an adaptive approach for the smoothing constant calculation.
  • Performance evaluation via Monte Carlo simulations and run-length profiles.

Main Results:

  • The proposed AEWMA chart effectively detects shifts in process dispersion.
  • An unbiased estimator improves the detection of increasing and decreasing dispersion shifts.
  • Demonstrated superior efficiency compared to the EWMA-S² dispersion chart.

Conclusions:

  • The new AEWMA chart offers a practical and user-friendly solution for real-time process dispersion monitoring.
  • Its adaptive nature and improved shift detection capabilities make it valuable for industrial applications.
  • The chart's performance is validated through simulations and a real-life dataset application.