A novel EWMA-based adaptive control chart for industrial application by using hastings approximation.

Control charts are commonly used for process monitoring under the assumption that the variable of interest follows a normal distribution. However, this assumption is frequently violated in real-world applications. In this study, we develop an adaptive control chart based on the exponentially weighted moving average (EWMA) statistic to monitor irregular variations in the mean of the Truncated Transmuted Burr-II (TTB-II) distribution, employing Hastings approximation for normalization. We propose a continuous function for the adaptation of the smoothing constant. The performance of the proposed TTB-II distribution is compared with multiple existing distributions, including TB-II, TB-III, TB-XII, B-II, B-III, and B-XII, to demonstrate its competitive advantages. The run-length profiles, including the average run-length (ARL) and the standard deviation of run-length (SDRL), are computed under various parameter settings. The effectiveness of the proposed chart is evaluated using Monte Carlo (MC) simulations in terms of run-length profiles. The practical implementation of the proposed chart is demonstrated with a real dataset, illustrating the design and application procedures.