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.