# Application of Robust Estimators in Shewhart S-Charts

## TL;DR

This paper explores the use of robust estimators in Shewhart S-charts to improve process monitoring accuracy in the presence of non-normal data and outliers, enhancing detection power in quality control.

## Contribution

It introduces the application of robust estimators in Shewhart S-charts, demonstrating their superiority over conventional estimators under contaminated data conditions.

## Key findings

- Robust estimators improve detection power in Shewhart S-charts.
- They are more effective against data contamination and outliers.
- Robust methods lead to quicker identification of process disturbances.

## Abstract

Maintaining the quality of manufactured products at a desired level is known to increase customer satisfaction and profitability. Shewhart control chart is the most widely used in statistical process control (SPC) technique to monitor the quality of products and control process variability. Based on the assumption of independent and normally distributed data sets, sample mean and standard deviation statistics are known to be the most efficient conventional estimators to determine the process location and scale, respectively. On the other hand, there is not guarantee that the real-world process data would be normally distributed: outliers may exist, and/or sampled population may be contaminated. In such cases, efficiency of the conventional estimators is significantly reduced, and power of the Shewhart charts may be undesirably low, e.g. occasional outliers in the rational subgroups (Phase I dataset) may drastically affect the sample mean and standard deviation, resulting a serious delay in detection of inferior products (Phase II procedure). For more efficient analyses, it is required to use robust estimators against contaminations. Consequently, it is determined that robust estimators are more efficient both against diffuse localized and symmetric-asymmetric contaminations, and have higher power in detecting disturbances, compared to conventional methods.

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Source: https://tomesphere.com/paper/1812.11132