Design and analysis of exponentially weighted moving average control charts for monitoring the variability of log-normal processes with estimated parameters

In statistical process control (SPC), the control chart is a quite popular technique to monitor the process efficacy. From a statistical point of view, the control chart is considered superior if it has an effective structure withholding property of the resistance against infrequent situations in a practical environment. The current study is designed for the same purpose for observing the dispersion parameter of log-normal distribution by using the structure of an exponentially weighted moving average (EWMA) chart. For the extensive study, EWMA range, EWMA standard deviation, EWMA Qn, EWMA Sn, EWMA mean absolute deviation, and EWMA transform standard deviation control charts are proposed. Properties of the run-length profile of the proposed designed structures based on different existing estimators as well as a newly transformed dispersion estimator for log-normal standard deviation are evaluated. The results indicate that the newly developed scheme outperforms the competitors when the dispersion parameter of the log-normal distribution attains a large value. A real-life application is also provided to validate how the developed design can be used in practice.