An improved adaptive EWMA control chart for monitoring time between events with application in health sector.

Nonconforming events rarely occur in high‐quality processes, and the time between events (TBE$TBE$) is likely to be followed by a skewed distribution, such as an exponential distribution. This paper proposes the upper and lower‐sided improved adaptive exponentially weighted moving control charts for monitoring TBE$TBE$ data modeled by the exponential distribution. The proposed control charts are labeled as IAEWMATBE$IAEWM{A_{TBE}}$ control charts, that is, the IAEWMATBEU$IAEWMA_{TBE}^U$ and IAEWMATBEL$IAEWMA_{TBE}^L$ control chart, respectively. The IAEWMATBEU$IAEWMA_{TBE}^U$ control chart detects the upward shifts, while the IAEWMATBEL$IAEWMA_{TBE}^L$ control chart identifies the downward shifts in the process. The Monte Carlo simulations are used to approximate the run length distribution of the proposed control charts. Numerical results associated with various performance measures, such as average run length (ARL$ARL$), standard run length (SDRL$SDRL$), median run length (MRL$MRL$), extra quadratic loss (EQL$EQL$), relative average run length (RARL$RARL$), and performance comparison index (PCI$PCI$) are computed. The proposed control charts compared to the respective existing control charts, such as AEWMATBE$AEWM{A_{TBE}}$, IEWMATBE$IEWM{A_{TBE}}$, REWMATBE$REWM{A_{TBE}}$, and ShewhartTBE${\rm{Shewhar}}{{\rm{t}}_{TBE}}$ control charts, at a single shift, as well as over a specified range of shifts. The comparison reveals that the proposed control charts outperform the existing control charts for both single specified shifts and over a certain range of shifts. Finally, real‐life data of hospital stay time for male patients with traumatic brain injury are analyzed for the applicability of the IAEWMATBEU$IAEWMA_{TBE}^U$ control chart in the health sector. [ABSTRACT FROM AUTHOR]