An overview and comparative analysis of synthetic control charts

Abstract

Synthetic control charts have emerged as an effective alternative in Statistical Process Control for detecting small and moderate shifts in process parameters. By integrating a Shewhart-type chart with a conforming run length (CRL) mechanism, these charts combine the simplicity of classical methods with improved sensitivity. This paper presents a comprehensive theoretical and empirical investigation of synthetic control charts. Exact and approximate expressions for performance measures, including Average Run Length (ARL) and variance of run length, are derived using probabilistic and Markov chain approaches. A detailed comparative analysis with the Shewhart Control Chart and EWMA Chart is conducted through simulation studies. The results demonstrate that synthetic charts outperform traditional Shewhart charts and are competitive with memory-type charts in detecting moderate process shifts, while maintaining lower variability in detection time. The study highlights the practical relevance, efficiency, and adaptability of synthetic control charts in modern quality monitoring applications.