On designing a progressive mean chart for efficient monitoring of process location

Variation is an important phenomenon of the output of every manufacturing and production process. To deal with the natural and special cause variations in the process, quality practitioners mostly apply control charts. There have been regular advancements over time in the design structures of these charts such as runs rules, fast initial response, sampling mechanisms among many others. In this article, auxiliary-information-based progressive mean (AIB-PM) control chart has been proposed, in which study variable is found correlated with another auxiliary variable. The development of the proposed AIB-PM structure utilises both the study and auxiliary variables. It is based on the regression estimator to introduce an unbiased and efficient estimate of the location parameter of the study variable. The performance assessment is carried out using average run length as a metric under zero-state and steady-state modes. The proposed AIB-PM chart is compared with some existing competitors and found that it performs uniformly superior than the existing competitors at small and persistent shifts in the process mean. An illustrative example using a real data set is presented to show the implementation of the proposed method.