📝 SummarXiv

Abstract

In the practical industry, the most commonly used application of statistical analysis for monitoring the process mean is the control chart. Control charts are generated based on the presumption that we have a sample from a stable process. The control chart then provides a graphical display to test this presumption. In the existing estimator \textcolor{red}{$Mr$}, researchers use a technique involving repetitive sampling along with an auxiliary variable for detecting and monitoring the statistical process mean. The existing control chart, namely \textcolor{red}{$Mr$}, is based on the regression estimator of the mean using a single auxiliary variable $X$. We propose the \textcolor{red}{$Mrep$} chart using a ratio-product exponential type estimator, and the \textcolor{red}{$Mrwp$} chart with a more efficient difference-cum-exponential type estimator used in quality control for improving the process mean in terms of $ARL$. Then we compare the proposed charts \textcolor{red}{$Mrep$} and \textcolor{red}{$Mrwp$} with the existing \textcolor{red}{$Mr$} chart in terms of $ARL$. Using $ARL$ as a performance measure, better results of the proposed charts are observed for detecting shifts in the mean level of the characteristic of interest. Moreover, Monte Carlo simulation in terms of repetitive sampling is used for quality control charting and statistical process control for the betterment of the process mean.