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Efficient bivariate EWMA charts for monitoring process dispersion
Author(s) -
OseiAning Richard,
Abbasi Saddam Akber
Publication year - 2020
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2569
Subject(s) - ewma chart , bivariate analysis , statistics , control chart , x bar chart , mathematics , dispersion (optics) , standard deviation , chart , statistical process control , multivariate normal distribution , multivariate statistics , process (computing) , computer science , physics , optics , operating system
Abstract To ensure high quality standards of a process, the application of control charts to monitor process performance has become a regular routine. Multivariate charts are a preferred choice in the presence of more than one process variable. In this article, we proposed a set of bivariate exponentially weighted moving average (EWMA) charts for monitoring the process dispersion. These charts are formulated based on a variety of dispersion statistics considering normal and non‐normal bivariate parent distributions. The performance of the different bivariate EWMA dispersion charts is evaluated and compared using the average run length and extra quadratic loss criteria. For the bivariate normal process, the comparisons revealed that the EWMA chart based on the maximum standard deviation ( SMAX E ) was the most efficient chart when the shift occurred in one quality variable. It also performed well when the sample size is small and the shift occurred in both quality variables. The EWMA chart based on the maximum average absolute deviation from median ( MDMAX E ) performed better than the other charts in most situations when the shift occurred in the covariance matrix for the bivariate non‐normal processes. An illustrative example is also presented to show the working of the charts.