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The X̄ Chart

The X̄ Chart

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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Related Experiment Video

Updated: Jun 9, 2025

Design and Optimization Strategies of a High-Performance Vented Box

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Published on: June 9, 2023

Bayesian control chart using variable sample size with engineering applications.

Imad Khan¹, Atif M Alamri², Abdullah M Almarashi³

¹Abdul Wali Khan University Mardan, Mardan, Pakistan.

Scientific Reports

|October 21, 2024

Summary

This study introduces an Adaptive Exponential Weighted Moving Average (AEWMA) control chart with Variable Sample Size (VSS) using Bayesian methods. The new chart offers improved detection and fewer false alarms in dynamic manufacturing environments.

Keywords:

ARL Bayesian approach Control charts Log normal Max-EWMA SDRL

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Area of Science:

Industrial Engineering
Statistical Quality Control
Operations Research

Background:

Traditional statistical process control (SPC) methods often struggle with dynamic manufacturing environments.
Existing Bayesian EWMA and AEWMA charts with fixed sample sizes have limitations in responsiveness and detection.

Purpose of the Study:

To propose an innovative Adaptive Exponential Weighted Moving Average (AEWMA) control chart that incorporates Variable Sample Size (VSS) under a Bayesian methodology.
To enhance the responsiveness and effectiveness of statistical process control in dynamic manufacturing settings.

Main Methods:

Development of an Adaptive Exponential Weighted Moving Average (AEWMA) control chart using Variable Sample Size (VSS).
Integration of an integer linear function for dynamic sample size adjustment based on the AEWMA statistic.
Incorporation of the smoothing constant from an EWMA chart to improve monitoring responsiveness.
Extensive simulations comparing the proposed chart against existing Bayesian EWMA and AEWMA charts with Fixed Sample Size (FSS).

Main Results:

The proposed Bayesian VAEWMA control chart demonstrates superior performance compared to existing methods.
The new chart exhibits enhanced sensitivity for detection improvement.
A significant decrease in the false alarm rate was observed with the proposed chart.
The Bayesian VAEWMA chart proved to be more effective overall in simulations.

Conclusions:

The findings support the need for dynamic statistical process control tools in dynamic manufacturing processes.
Adaptive SPC methods are crucial for optimizing control in modern manufacturing environments.
A real data application validated the effectiveness and optimal performance of the proposed Bayesian VAEWMA control chart.