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 (X) over bar chart and the conforming run length chart. Like the Shewhart (X) over bar chart, the synthetic chart is used to detect the proc ess mean shift delta. We found from intensive performance tests that the sy nthetic control chart: consistently produces smaller out-of-control average run lengths (ARL's) than the Shewhart (X) over bar chart (with or without supplementary runs rules) for any size-of delta when the false alarm rate i s held at a specified value. Compared to the Shewhart (X) over bar chart, w hen delta is moderate (between 0.5 sigma and 1.5 sigma), the synthetic cont rol chart can reduce the out-of-control ARL by nearly half. The synthetic c ontrol chart also outperforms the exponentially weighted moving average (EW MA) chart and the joint (X) over bar-EWMA charts when delta is greater than 0.8 sigma.