Reassessment of performance evaluation of EWMA control chart for exponential process

Memory control charts or charts, such as cumulative sums and exponentially weighted moving average (EWMA), are widely used for tracking minor to moderate changes in process parameters. The literature presented an EWMA chart for monitoring exponential processes, assuming probability limits to determine both in- and out-of-control average run length (ARL). The use of probability limits for memory charts is an incorrect method. So, we are aiming to correct the EWMA chart by Aslam et al. and the proposed EWMA chart (represented by (Formula presented.)) for the exponential process using the run-length (RL) method based on the simulation method instead of the probability-based method. The ARL, standard deviation of RL, and median of RL are used to evaluate the proposed chart's performance. For practical consideration of the proposed chart, a real-world example of a urinary tract infection is also presented.