An Improved Charting Scheme to Monitor the Process Mean Using Two Supplementary Variables

Abstract

A control chart is the most well-known statistical monitoring tecnique to address unfavourable process parameter (s) changes. Quality practitioners always desire a charting device that promptly identifies the undesired changes in the process. This study intends to design a sensitive homogeneously weighted moving average chart using two supplementary variables (hereafter, TAHWMA). The two supplementary variables are correlated with the study variable in the form of a regression estimator, which is an efficient and unbiased estimator for the process mean. The suggested TAHWMA charting structure is checked out and compared in terms of appearance and non-appearance of multicollinearity amidst the two additional variables. Average run length-related measures are taken as performance measures. It is observed that the proposed TAHWMA scheme performs effectively when the two supplementary variables have no collinearity. A comprehensive comparison between the proposed TAHWMA and existing charts is also carried out, showing the proposed’s supremacy over existing counterparts. For execution purposes, two illustrative examples, one belonging to carbon fibre manufacturing-related data and the other using a simulated dataset and where our simulated dataset belongs to symmetrical distribution, are also presented for the application of the recommended TAHWMA chart.

Keywords

• average run length
• control chart
• multicollinearity
• regression estimator
• supplementary variable