New robust location control charts for unknown process distribution with practical significance

In this study, we have proposed skewness correction-based various location control charts for monitoring process characteristics with unknown probability distribution. The location control charts include mean, median, and Hodges–Lehmann. For designing purposes, we have involved advanced skewness correction methods to relax from restricted assumptions. To deal with the situations where parameters of process characteristics are unknown, we have considered various robust location and dispersion estimators. Afterward, performance of proposed skewness correction-based location control charts is measured using control limits, and actual false alarm rate as performance measures. The performance measures of control charts are calculated through Monte Carlo simulation approach by considering the variant symmetric and skewed distributions. Results revealed that control limits of the proposed control charts are observed closest to exact control limits. Also, proposed skewness correction-based location control charts are robust in terms of maintaining the actual false alarm rate close to desire level as compared the existing control charts. Among various proposed location control charts, median and Hodges–Lehmann control charts are observed excellent relative to the others when unknown symmetric distribution is leptokurtic. Among various dispersion estimators, interquartile range and Gini mean difference played maximum role with control charts to maintain the actual false alarm rate. Besides, a real data example from Portland cement manufacturing process is also included to endorse the ability of the proposed skewness correction location control charts.