Control charts for paired differences: d and S-d charts

摘要

Control chart procedures for monitoring paired variables are sparse in the iterature. After considering the average run length properties of (d) over bar chart, which monitors the mean of the differences between paired variables, we propose a new chart based n S-d, the subgroup standard deviations of the differences. Our findings show that the (d) over bar 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) over bar and S-d charts perform better than existing bivariate control charts for detecting shifts in mean and vaxiance/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.