A Synthetic Control Chart for Detecting Small Shifts in the Process Mean

This paper presents a synthetic control chart that is an integration of the Shewhart X̄ chart and the conforming run length chart. Like the Shewhart X̄ chart, the synthetic chart is used to detect the process mean shift, δ. We found from intensive performance tests that the synthetic control chart consistently produces smaller out-of-control average run lengths (ARL's) than the Shewhart X̄ chart (with or without supplementary runs rules) for any size of δ when the false alarm rate is held at a specified value. Compared to the Shewhart X̄ chart, when δ is moderate (between 0.5σ and 1.5σ), the synthetic control chart can reduce the out-of-control ARL by nearly half. The synthetic control chart also outperforms the exponentially weighted moving average (EWMA) chart and the joint X̄-EWMA charts when δ is greater than 0.8σ.