Homogeneously weighted moving average-variance control chart using auxiliary information

Abstract

In this study, a variance control chart is proposed with some modifications in terms of the rapid detection of process shifts by using the homogenously weighted moving average ($\mathit{HWMA}$) statistic by using the information from an auxiliary variable. The proposed $\mathit{HWMA}$ chart is a new memory type variance control chart with a three-parameter log transformation that operates by assigning the specified weights to the most recent value. All previous samples are allotted with an equal proportion of the remaining smoothing parameter weight. The remaining weights put their effect as a counterpart within the smoothing parameter and the current observations take the maximum of it. To study the performance of the proposed chart the respective run length properties are determined by Monte Carlo simulations and extensively presented in the tables. The comparison has been made with the existing exponentially weighted moving average ($\mathit{EWMA}$) variance control chart. It is figured out that the proposed control chart is sensitive to process shift by using the auxiliary information with a high degree of correlation. The real-life dataset is selected from an industrial production environment to demonstrate the implementation of the proposed chart.

Keywords:

• Homogenous weights
• Exponential weights
• Logarithmic transformation
• Auxiliary information
• Control chart

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62P30

Acknowledgments

The authors are indebted to the anonymous reviewer(s) for their valuable suggestions that to improve the quality of the manuscript.