A homogeneously weighted moving average control chart for monitoring time between events

In high-quality processes, non-conforming events rarely occur, and the time between events (TBE) is more likely to follow a skewed distribution, such as gamma distribution. This paper proposes a gamma distribution-based one-sided homogeneously weighted moving average control chart for monitoring the TBE. The proposed control chart is known as the HWMA_TBE control chart. The HWMA_TBE control chart monitors the downward shifts in the process, that is, a decrease in inter-arrival time that can lead to the process deterioration. The Monte Carlo simulation approach is used to compute specific performance indicators, such as average run length (ARL), standard deviation run length (SDRL), extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI). Based on these performance indicators, the HWMA_TBE control chart is compared to some competing control charts. The comparison suggests that the HWMA_TBE control chart is more efficient than the competing control charts. Moreover, this paper also investigates the robustness of the HWMA_TBE control chart, which indicates that the HWMA_TBE control chart is more robust than the competing control charts. In the end, two examples are provided, one with boring machine failure data and the other with breast cancer survival data, to evaluate the implementation of the HWMA_TBE control chart for practical situations.