# Control chart for geometrically distributed data based on Bayesian fast double bootstrap

## TL;DR

This paper introduces a new Bayesian fast double bootstrap method to improve process control for geometrically distributed data, especially with small sample sizes.

## Contribution

The novel Bayesian fast double bootstrap approach enhances parameter estimation in g-charts for small samples and high-quality monitoring.

## Key findings

- BFDB outperforms MVU estimators in sensitivity and computational efficiency for small sample sizes.
- BFDB effectively detects large process shifts and improves accuracy in process monitoring.

## Abstract

Accurate parameter estimation is a critical component of effective process control using g charts. While traditional methods like maximum likelihood and Bayesian estimation are widely used, th ey may exhibit limitations in small sample size scenarios, leading to inaccurate parameter estimates. To address these challenges, minimum variance unbiased (MVU) estimators have been developed. For specific conditions, such as limited data and no nonconforming items, bootstrap-based Bayesian estimators offer a computational alternative. However, these estimators may struggle to detect significant process shifts, particularly in the presence of large deviations. This research introduces a novel Bayesian fast double bootstrap approach for parameter estimation in g-charts. By efficiently handling small sample sizes and effectively detecting large process shifts, this method aims to significantly enhance the accuracy and reliability of process monitoring. The proposed approach leverages the strengths of both bootstrap and double bootstrap techniques, while addressing their limitations through a computationally efficient algorithm. This advancement is expected to contribute to improved process control and quality assurance in various industrial applications. Key points:•A Bayesian fast double bootstrap (BFDB) approach was developed for parameter estimation in process monitoring, particularly for small sample sizes. Comparative analysis with minimum variance unbiased (MVU) estimators demonstrated the superior sensitivity and computational efficiency of BFDB for process monitoring•A comparative analysis of BFDB and MVU parameter estimation methods revealed that BFDB consistently outperformed MVU in high-quality process monitoring scenarios.

A Bayesian fast double bootstrap (BFDB) approach was developed for parameter estimation in process monitoring, particularly for small sample sizes. Comparative analysis with minimum variance unbiased (MVU) estimators demonstrated the superior sensitivity and computational efficiency of BFDB for process monitoring

A comparative analysis of BFDB and MVU parameter estimation methods revealed that BFDB consistently outperformed MVU in high-quality process monitoring scenarios.

Image, graphical abstract