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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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Monitoring of zero-inflated binomial processes with a DEWMA control chart.

Vasileios Alevizakos¹, Christos Koukouvinos¹

¹Department of Mathematics, National Technical University of Athens, Zografou, Athens, Greece.

Journal of Applied Statistics

|June 16, 2022

Summary

This study introduces the zero-inflated binomial double exponentially weighted moving average (ZIB-DEWMA) control chart for quality monitoring in high-yield processes with many zeros. The new ZIB-DEWMA chart demonstrates effective detection of shifts in process parameters.

Keywords:

Average run-length (ARL)ZIB-DEWMA chart ZIB-EWMA chart ZIB-Shewhart chart zero-inflated binomial (ZIB) distribution

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Area of Science:

Statistical Process Control
Quality Engineering
Industrial Statistics

Background:

High-yield processes often exhibit count data with a large number of zero observations.
Traditional binomial models are inadequate for such data; zero-inflated binomial (ZIB) models are more appropriate.
ZIB models account for random shocks (probability θ) and binomial variation (proportion p).

Purpose of the Study:

To further investigate the zero-inflated binomial exponentially weighted moving average (ZIB-EWMA) control chart.
To propose a novel control chart, the ZIB-DEWMA, for monitoring ZIB data.
To assess the performance of these charts in detecting shifts in ZIB parameters θ and/or p.

Main Methods:

Detailed study of the ZIB-EWMA control chart.
Development and proposal of the ZIB-DEWMA control chart.
Simulation study to compare ZIB-DEWMA against ZIB-Shewhart, ZIB-EWMA, and ZIB-CUSUM charts.
Evaluation of detection capabilities for individual and simultaneous shifts in θ and p.

Main Results:

The ZIB-DEWMA chart is effective in detecting upward shifts in the zero-inflated binomial parameters.
Comparative analysis through simulations quantifies the performance of the proposed ZIB-DEWMA chart.
The study provides insights into the sensitivity of different control charts for ZIB data.

Conclusions:

The ZIB-DEWMA control chart offers a valuable tool for quality monitoring in processes with excess zeros.
The proposed chart shows competitive or superior performance compared to existing ZIB charts.
An illustrative example demonstrates the practical applicability of ZIB control charts in real-world scenarios.