A general charting scheme for monitoring serially correlated data with short-memory dependence and nonparametric distributions

Abstract

Traditional statistical process control charts are based on the assumptions that process observations are independent and identically normally distributed when the related process is In-Control (IC). In recent years, it has been demonstrated in the literature that these traditional control charts are unreliable to use when their model assumptions are violated. Several new research directions have been developed, in which new control charts have been proposed for handling cases when the IC process distribution is nonparametric with a reasonably large IC data, when the IC process distribution is unknown with a small IC data, or when the process observations are serially correlated. However, existing control charts in these research directions can only handle one or two cases listed above, and they cannot handle all cases simultaneously. In most applications, it is typical that the IC process distribution is unknown and hard to be described by a parametric form, the process observations are serially correlated with a short-memory dependence, and only a small to moderate IC dataset is available. This article suggests an effective charting scheme to tackle such a challenging and general process monitoring problem. Numerical studies show that it works well in different cases considered.