# A parametric bootstrap control chart for Lindley Geometric percentiles

## TL;DR

A new control chart using parametric bootstrap improves quality control for skewed Lindley geometric distributions in industrial processes.

## Contribution

A novel parametric bootstrap control chart for Lindley geometric percentiles is introduced for better process monitoring.

## Key findings

- The new control chart is sensitive to changes in Lindley geometric distribution parameters.
- Subgroup size, percentiles, and significance levels significantly affect control limits.
- The chart performs consistently across different percentiles and distribution parameters.

## Abstract

Control charts are vital for quality control and process monitoring, helping businesses identify variations in production. Traditional control charts, like Shewhart charts, may not work well for skewed distributions, such as the Lindley geometric distribution (LG). This study introduces a new control chart that uses parametric bootstrap techniques to monitor percentiles of the LG distribution, providing a more effective quality control method. The LG distribution is useful for modeling material strength and failures, especially in structural design, where lower percentiles indicate reduced tensile strength. We conducted extensive simulations to assess the proposed control chart’s effectiveness, considering various distribution parameters, percentile values, Type I error rates, and sample sizes. Our findings highlight how subgroup size, percentiles, and significance levels affect control limits, stressing the need for careful parameter selection in monitoring processes. The results show that the new control chart is highly sensitive to changes in LG distribution parameters and performs consistently across different percentiles. This suggests its practical relevance and robustness for industrial applications in quality control. Future research should explore its performance in real-world production settings to confirm its efficiency and reliability.