A control chart using an auxiliary variable and repetitive sampling for monitoring process mean

Abstract

In this paper, a new control chart is proposed by using an auxiliary variable and repetitive sampling in order to enhance the performance of detecting a shift in process mean. The product-difference type estimator of the mean is plotted on the proposed control chart, which utilizes the information of an auxiliary variable correlated with the main quality variable. The proposed control chart is based on the outer and inner control limits so that repetitive sampling is allowed when the plotted statistic falls between the two limits. The average run length (ARL) of the proposed control chart is evaluated using the Monte Carlo simulation. The proposed control chart is compared with the Riaz M control chart and the results show the outperformance of the proposed control chart in terms of the ARL.

Keywords:

• auxiliary variable
• bivariate normal
• process mean
• repetitive sampling

Acknowledgements

The authors are deeply thankful to the associate editor and reviewers for their valuable suggestions.

Additional information

Funding

This research was supported by the National Research Foundation of Korea (Project no. NRF-2013R1A2A2A03068323).