In this paper, we purpose a monitoring scheme of individual observation that can be modeled as a first-order vector autoregressive process and develop it to mean square successive difference matrix based on residuals. Due to the effect of shift in mean process on VAR residual charts, we investigate the T2-type charts performance of T2VAR(1) residual and T2D control charts as an individual observation. Then we compare both T2-type charts using upper control limit approximation with α=0.005 (fix) based simulation. From the results of comparison, it shows that the T2D chart for a small to moderate level of shift in the process mean vector gives a better performance than the T2VAR(1) charts. Conversely, the T2D charts indicate a fault detection in large level of shift and the T2VAR(1) chart is more reliable on outliers detection. Thus, the result may not only provide a good option for quick response on monitoring scheme for residual, but also provide the way to avoid fault detection in a multivariate process.

Original languageEnglish
Pages (from-to)3491-3499
Number of pages9
JournalApplied Mathematical Sciences
Issue number69-72
Publication statusPublished - 2014


  • T and Tchart
  • Vector autoregressive models (VAR) residual


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