Generalized Hotelling T² control chart based on bivariate ranked set techniques with runs rules

In this study, we have introduced a generalized Hotelling T² control chart based on bivariate ranked set techniques with runs rules to identify small and moderate variations in a process mean vector. To achieve this aim, plotting statistic and control limits are formulated in generalized approaches. For evaluation purposes, power and power curves are used as performance indicators. Afterwards, power curves are drawn through Monte Carlo simulation procedures by taking into account different choices of factors. A detailed discussion about the role of factors on the performance of the proposed generalized control chart is included. Furthermore, the proposed generalized control chart with double bivariate ranked set techniques is noted to be superb compared to the other cases of single bivariate ranked set techniques. Among single and double versions of bivariate ranked set techniques, the proposed generalized control chart on the basis of median bivariate ranked set techniques is recorded as more efficient relative to the other choices under consideration. Also, comparative analysis shows that the proposed generalized control chart with supplementary runs rules performs outstandingly for detection of small and moderate variations relative to existing control charts. Special cases of the proposed generalized control chart are elaborated to highlight its features for accommodating the existing control charts. To amplify the uses and advantages of the proposed generalized control chart, a real-world example from agriculture is presented.