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All Journal Stationer: Journal of Statistical Innovations and Applications
Muhammad Solihin Sahal
Universitas Islam Negeri Abdul Mutholib Sangadji, Indonesia

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Development of a Robust Shrinkage Empirical-Bayes P-Chart for Heterogeneous Proportion Data Muhammad Solihin Sahal
Stationer: Journal of Statistical Innovations and Applications Vol. 1 No. 1 (2026): Stationer: Journal of Statistical Innovations and Applications
Publisher : Stationer: Journal of Statistical Innovations and Applications

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Abstract

This study develops a Robust Shrinkage Empirical-Bayes P-Chart (RSEB p-chart) for monitoring proportions when subgroup sizes differ and observed proportions are heterogeneous. The classical p-chart assumes binomial variation around a stable process proportion, but real educational, health, and service data often show extra-binomial variation and unstable small-sample proportions. The proposed method combines a robust center line based on the median proportion with empirical-Bayes shrinkage of subgroup proportions. The empirical illustration uses the public STAR98 educational assessment dataset available through statsmodels. Results show that the proposed chart stabilizes proportions across subgroup sizes and provides interpretable control limits. The article contributes a transparent p-chart development for proportion monitoring in heterogeneous public-sector data.
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