Control charts for monitoring fault signatures: Cuscore versus GLR

It is commonly assumed that an assignable cause may shift a process mean persistently to an unknown but constant value. However, there are situations such that a mean change is not persistently constant but time varying, which is known as the signature of a fault. Different forms of fault signatures may arise, especially when a residuals control chart is used to monitor an autocorrelated or closed-loop controlled process. Incorporating a priori knowledge of a fault signature, fault-sensitized control charts may be developed. In this paper, we investigate two control charts of this kind: generalized likelihood ratio (GLR) and cumulative score (Cuscore) charts. A sine wave representing a bounded signal and a linear trend representing an unbounded signal are used as fault signatures for investigation purposes. Two different cases are analyzed, a known fault signature and parameter and a known fault signature but unknown parameter. Both the initial performances and steady-state performances of these charts are analyzed. The former case is somewhat artificial since it is synchronizing the control statistic and the fault signature; the latter one is more realistic since time of the occurrence of a fault is unknown. Simulation results show that GLR charts are robust to unknown signal start times and perform better than the alternatives for the cases compared.