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

Abstract

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.

A review of ranked set sampling and modified methods in designing control charts

“…proposed and assessed the performance of adaptive control charts based on the RSS method. Mehmood et al 167 . developed the generalized Hotelling T 2 control chart by using the BVRST techniques with runs rules for detecting small and moderate variations in the process mean vector.…”

“…Santore et al 166 proposed and assessed the performance of adaptive control charts based on the RSS method. Mehmood et al 167 developed the generalized Hotelling T 2 control chart by using the BVRST techniques with runs rules for detecting small and moderate variations in the process mean vector. Later, Mehmood et al 65 proposed the Hotelling T 2 control chart based on different BVRST schemes with the classical runs rule.…”

A variable sample size side-sensitive synthetic coefficient of variation chart

“…Control charts efficiently detect special causes that result in abnormal variation in a process by detecting changes in specific statistical parameters. In most cases, shifts in the mean ( μ ) and standard deviation ( σ ) are monitored (see, for instance, Abbas et al, 2020; Amin et al, 2021; Haq et al, 2023; Javaid et al, 2023; Mehmood et al, 2021; Shafqat et al, 2021; and Umar et al, 2019). However, such an approach was found to result in erroneous conclusions when the process does not have a consistent μ , in addition to having a σ that varies with μ .…”

Application of Hotelling T2 Control Diagram to Analyze Drinking Water Quality Control at Perumda Tirtauli Pematang Siantar City

“…Process capability analysis is a statistical method that looks at variability against specifications to see if it can be used to reduce variability. (Mehmood et al, 2021).…”