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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.
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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
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Quality Control01:05

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Quality control is one of the three cyclical quality assurance activities that help keep a system under statistical control. Typical quality control activities include creating quality control charts, conducting proficiency testing, and documenting and archiving results.
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A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
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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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Upper quantile-based CUSUM-type control chart for detecting small changes in image data.

Anik Roy1, Partha Sarathi Mukherjee1

  • 1Indian Statistical Institute, Kolkata, India.

Journal of Applied Statistics
|September 4, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new CUSUM-type control chart for monitoring grayscale images, improving detection of small changes even with noise. The enhanced method offers superior performance for online image analysis in various fields.

Keywords:
62P30Anomaly detectionCUSUM chartedge preserving smoothingfault regionnoisy imagesparse changes

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Area of Science:

  • Statistical Process Control
  • Image Analysis
  • Computer Vision

Background:

  • Traditional image monitoring control charts struggle with detecting subtle changes in small image regions, especially with noise or near object edges.
  • Small intensity variations in images, common in manufacturing and diagnostics, often evade detection by conventional methods.
  • Human visual inspection is insufficient for identifying minute alterations in industrial or medical imaging.

Purpose of the Study:

  • To develop an advanced CUSUM-type control chart for effective online monitoring of grayscale images.
  • To enhance the detection capabilities for small and localized changes within image data.
  • To provide a robust solution for image monitoring that performs well under noisy conditions.

Main Methods:

  • Proposed a Cumulative Sum (CUSUM)-type control chart tailored for grayscale image monitoring.
  • Utilized upper quantiles of local CUSUM statistics to adapt detection sensitivity for varying change magnitudes.
  • Integrated a novel jump-preserving image smoothing technique to mitigate noise effects while preserving critical image features.

Main Results:

  • The proposed control chart demonstrates superior performance in detecting small regional changes compared to traditional methods.
  • Effective noise handling capability ensures reliable monitoring even with low to moderate image noise.
  • Numerical comparisons validate the enhanced sensitivity and accuracy of the new monitoring technique.

Conclusions:

  • The developed CUSUM-type control chart offers a significant advancement for online grayscale image monitoring.
  • Its ability to detect subtle changes and handle noise makes it valuable for applications in manufacturing, medical diagnostics, and satellite imaging.
  • The proposed method provides a robust and effective tool for researchers and practitioners in image analysis and quality control.