Distribution-free Phase II triple EWMA control chart for joint monitoring the process location and scale parameters

ABSTRACT

Distribution-free or nonparametric control charts are used for monitoring the process parameters when there is a lack of knowledge about the underlying distribution. In this paper, we investigate a single distribution-free triple exponentially weighted moving average control chart based on the Lepage statistic (referred as TL chart) for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous distribution. The design and implementation of the proposed chart are discussed using time-varying and steady-state control limits for the zero-state case. The run-length distribution of the TL chart is evaluated by performing Monte Carlo simulations. The performance of the proposed chart is compared to those of the existing EWMA-Lepage (EL) and DEWMA-Lepage (DL) charts. It is observed that the TL chart with a time-varying control limit is superior to its competitors, especially for small to moderate shifts in the process parameters. We also provide a real example from a manufacturing process to illustrate the application of the proposed chart.

KEYWORDS:

• A verage run-length
• distribution-free control chart
• Lepage statistic
• Phase II
• TEWMA chart

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30

Acknowledgments

The authors would like to thank the Editor and the referees for their useful comments which resulted in improving the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).