Control chart for joint monitoring mean and variance of a stationary process

As a newly proposed control scheme in SPC, adaptive-loss-function (AL) control chart is a single chart for monitoring process mean and variance simultaneously (Wang and Wu, 2004). It has demonstrated considerable reductions in average run length (ARL) to signal process shifts for independent observations. This article is a follow-up effort to extend the AL chart to a stationary process of AR(1). Under an AR(1) model, the application of the original AL chart is addressed by a residual approach conveniently. Through numerical comparisons, it is found that the AL chart by residual approach is a preferable choice over a wide range of process shifts relative to other two schemes. Generally, the superiority is more evident for moderate to large mean shift in case of positive correlation, and for small to moderate mean shift in presence of negative correlation