A robust hybrid exponentially weighted moving average chart for monitoring time between events.

Monitoring time between events (TBE${\rm{TBE}}$) is an essential aspect of the high‐yield processes where the events of interest rarely occur. This study proposes a one‐sided scheme of a hybrid exponentially weighted moving average (HEWMA) chart for monitoring TBE${\rm{TBE}}$, where it is assumed that the TBE${\rm{TBE}}$ observations follow a gamma distribution. This chart is symbolized as the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart. The HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart detects the downward shift, that is, a decrease in the interarrival times that can lead to a deterioration of the process. A simulation study is carried out for the numerical results, and one‐sided HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart is evaluated along with one‐sided triple EWMA${\rm{EWMA}}$ (TEWMATBE)${\rm{TEWM}}{{\rm{A}}_{{\rm{TBE}}}})$, double EWMA${\rm{EWMA}}$(DEWMATBE)${\rm{(DEWM}}{{\rm{A}}_{{\rm{TBE}}}})$, EWMA${\rm{EWMA}}$(EWMATBE)${\rm{(EWM}}{{\rm{A}}_{{\rm{TBE}}}})$, double GWMA${\rm{GWMA}}$(DGWMATBE)${\rm{(DGWM}}{{\rm{A}}_{{\rm{TBE}}}})$, and GWMA${\rm{GWMA}}$(GWMATBE)${\rm{(GWM}}{{\rm{A}}_{{\rm{TBE}}}})$ charts. The results show that the one‐sided HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart outperforms its rivals, particularly in the case of small‐to‐moderate downward shifts. Moreover, this study also investigated the robustness of the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart, where the true distribution of the TBE${\rm{TBE}}$ observations is assumed to be Weibull or lognormal, and it is found that the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart is reasonably robust. Finally, two examples are given to demonstrate how to use the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart in real‐world situations. [ABSTRACT FROM AUTHOR]