An Optimized Double-Sampling c Control Chart for Enhanced Monitoring of Process Nonconformities

Statistical Process Control (SPC) plays a vital role in monitoring manufacturing and service processes characterized by count data. The conventional Shewhart c-control chart is widely used for monitoring the number of nonconformities under the Poisson distribution; however, its performance deteriorates when detecting small and moderate process shifts. This study proposes an optimized Double-Sampling (DS) c-control chart that improves shift detection while maintaining a specified in-control Average Run Length (ARL₀). The chart design is formulated as a constrained optimization problem in which the out-of-control Average Run Length (ARL₁) is minimized subject to target ARL₀ and inspection efficiency requirements. Exact Poisson probabilities are employed to derive the operating characteristics, while the Average Sample Size (ASS) is used to evaluate inspection effort. Extensive numerical comparisons for various process means and shift magnitudes demonstrate that the proposed DS c-chart consistently achieves substantially lower ARL₁ values than the conventional single-sampling c-chart, particularly for small and moderate shifts, while maintaining the desired false-alarm performance. The proposed scheme provides an efficient, practical, and economically attractive alternative for monitoring Poisson-distributed process nonconformities.

Double-Sampling c-Control Chart; Statistical Process Control; Poisson Distribution; Average Run Length; Average Sample Size; Attribute Control Charts.

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