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Control charts for paired differences: d ¯ and S d charts
Author(s) -
Premarathna L.P. Nadeeka D.,
Godfrey A. Jonathan R.,
Govindaraju Kondaswamy
Publication year - 2017
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.2147
Subject(s) - control chart , statistics , chart , bivariate analysis , mathematics , ewma chart , covariance , standard deviation , statistical process control , econometrics , computer science , process (computing) , operating system
Control chart procedures for monitoring paired variables are sparse in the literature. After considering the average run length properties of the d ¯ chart, which monitors the mean of the differences between paired variables, we propose a new chart based on S d , the subgroup standard deviations of the differences. Our findings show that the d ¯ chart is powerful for monitoring the changes in the means and the S d chart is suitable for monitoring changes in the covariance structure. Furthermore, we show that the d ¯ and S d charts perform better than existing bivariate control charts for detecting shifts in mean and variance/covariance, respectively, when standards are known. The difference charts also performed well compared to common alternatives when the standards are unknown arising from a limited amount of Phase I data. An application of these difference charts in a finance context is illustrated using the returns of Apple Inc's stock and the S&P 500 index.