EWMA and DEWMA repetitive control charts under non-normal processes

Abstract

In this paper, we present a repetitive sampling method to construct control charts using exponentially weighted moving averages (EWMA) and double exponentially weighted moving averages (DEWMA) to monitor shift in the process. For non-normal processes, t-distribution with various degrees of freedom (i.e. $\text{df}=4,10,20,40,50$) is used as symmetric distribution, gamma distribution with unit scale parameter and various shape parameters (i.e. $0.5,1,2,3,4$) is used as positively skewed distribution and Weibull distribution with unit scale parameter and various shape parameters (i.e. 10 and 20) is used as negatively skewed distribution. We use Monte Carlo simulations to check whether the process is out of control. We use average run length as a tool to find the ability of proposed control charts to identify a shift earlier in a process, as compared to other control charts currently used to monitor the same type of process. The proposed control charts are applied to two real datasets.

KEYWORDS:

• Control charts
• EWMA statistic
• DEWMA statistic
• t distribution
• gamma distribution
• Weibull distribution

Acknowledgements

The authors are deeply thankful to the editor and reviewers for their valuable suggestions to improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.