Notes on shift effects for T2-type charts on multivariate ARMA residuals

Statistical process control (SPC) needs to be aided by computers in order to deal with dynamic systems. Hence, more knowledge on the complexity of this issue is needed. This paper discusses in general the shift effects of residuals from vector autoregressive moving average process for Shewhart-type, i.e. Hotelling T2-type charts (we call it H charts). Three types of parameter shift were considered: mean shift, covariance shift, and coefficient shift. The estimation effects were addressed. The discussions begin with the shift effects for residuals then for T2-type chart on residuals. The out-of-control distributions of the chart statistic were provided in this paper.