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Related Experiment Video

Updated: Dec 13, 2025

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Published on: November 24, 2021

Process monitoring using inflated beta regression control chart.

Luiz M A Lima-Filho¹, Tarciana Liberal Pereira¹, Tatiene C Souza¹

¹Departamento de Estatística, Universidade Federal da Paraíba, João Pessoa, Brazil.

|July 31, 2020

Summary

This study introduces a new control chart for quality control, utilizing an enhanced inflated beta regression model to effectively manage fractional data. The new chart demonstrates reliable performance in simulations and practical applications.

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Area of Science:

Statistical Process Control
Quality Management
Regression Modeling

Background:

Traditional control charts struggle with data confined to specific intervals like (0, 1].
The inflated beta regression model is suitable for analyzing proportions and fractions.
Existing models lack flexibility in handling the precision parameter within this framework.

Purpose of the Study:

To extend the inflated beta regression model by incorporating a regression structure for the precision parameter.
To develop a novel, model-based control chart for quality characteristics within the (0, 1] interval.
To assess the performance of the proposed estimators and control chart through simulations and an empirical case.

Main Methods:

Reparameterization of the inflated beta distribution for mean-indexed modeling.
Derivation of closed-form expressions for the score vector and Fisher's information matrix.
Development of a control chart using parameter estimates from the extended regression model.

Main Results:

The extended inflated beta regression model provides a robust framework for fractional data.
The proposed control chart effectively monitors quality characteristics within specified intervals.
Monte Carlo simulations confirm the performance of the model estimators and the control chart's run length distribution.

Conclusions:

The enhanced inflated beta regression model offers improved flexibility for statistical process control.
The new model-based control chart is applicable for quality control of fractional data.
The empirical application validates the practical utility of the proposed regression control chart.