A new SPRT chart for monitoring process mean and variance

This article proposes a new control chart (called the ABS SPRT chart) for Statistical Process Control (SPC) based on Sequential Probability Ratio Test (SPRT). This chart is able to monitor the mean and variance of a variable x simultaneously by inspecting the absolute sample shift |x−μ0| (where μ0 is the in-control mean or target value of x). The ABS SPRT chart is designed by an optimization algorithm, aiming at minimizing the Average Extra Quadratic Loss (AEQL) over the process shift domain. The results of intensive performance studies show that the ABS SPRT chart not only uniformly outperforms the CUSUM chart with a Variable Sample Size (VSS) feature, but is also more effective than a 2-SPRT scheme which incorporates a lower-sided SPRT chart and an upper-sided one. From a holistic viewpoint, the ABS SPRT chart detects process shifts in mean and variance faster than the VSS CUSUM chart and 2-SPRT scheme by more than 30% and 13%, respectively. Noteworthily, the design of an ABS SPRT chart is relatively easier than that of a VSS CUSUM chart, and much simpler than the design of a 2-SPRT scheme.