Enhanced Adaptive EWMA Control Chart to Observe Inverse Maxwell Process With Engineering and Healthcare Sector Applications

Conventional control chart schemes often assume normality when monitoring processes, a condition that is not consistently applicable. The aforementioned constraint is notably apparent in a variety of engineering dealings, especially when characterized by the prevalence of the inverse Maxwell process. An important development in the field of process monitoring is the growing importance of an adaptive exponentially weighted moving average ((Formula presented.)) control chart. This study proposed an (Formula presented.) control chart for inverse Maxwell processes, abbreviated as (Formula presented.). The (Formula presented.) chart is evaluated using several criteria, including average run length, median run length, and standard deviation run length. The comprehensive analysis includes extra quadratic loss, relative average run length, and performance comparison index. A two-step optimization procedure was utilized to identify the optimal design parameters, ensuring that the monitoring scheme is capable of effectively detecting both large and small shifts. To evaluate the effectiveness of the (Formula presented.) chart, it is compared to other charts in the same family, for inverse Maxwell distribution, such as (Formula presented.) control chart, and exponentially weighted moving average ((Formula presented.) control chart. The results indicate that the proposed (Formula presented.) chart exhibits higher efficiency compared to its competitors. To demonstrate the practical application of the proposed control chart, two real-life examples are provided, using brake pad failure data and the COVID-19 estimated reproduction number to demonstrate its utilization in an actual data set. The findings of our study reveal the significant role of the proposed chart in improving process monitoring. Its effectiveness in detecting shifts in different scenarios has been established, as evidenced by its successful use in practical settings.