Non-parametric Control Charts for Monitoring Serial Dependence based on Ordinal Patterns

We consider the problem of monitoring for the existence of serial dependence in real-valued and continuously distributed processes. These can exist when a process goes out-of-control. Besides, as many control charts are designed under the assumption of independent and identically distributed observations, the validity of this assumption needs to be checked. In the literature, the majority of studies handled this problem by utilizing a specific case of autoregressive moving-average time series models. Also a moving-window approach is often considered, which leads to the drawback that at least a window length of observations need to be collected before an out-of-control situation can be detected. Here, we utilize ordinal patterns and propose charts that are fully non-parametric and distribution-free, have a unique chart design, and can be used almost instantaneously at the start of process monitoring. The proposed control charts do not require any model fitting, thus eliminating the problems associated with estimation errors, but might be used as part of a Phase-I study. Through a comprehensive performance comparison study under various out-of-control scenarios, the effectiveness of the charts in uncovering serial dependence is shown and recommendations for selection are given. Implementations of the proposed charts are illustrated by using batch yield data from a chemical process.