A Self-Starting Control Chart for Multivariate Individual Observations.

Multivariate versions of cumulative sum, exponentially weighted moving average (EWMA), and Hotelling's T2 charts typically assume knowledge of the in-control process parameters or, with a new or changed process, use parameter estimates from an in-control reference sample of preliminary observations. In contrast, the self-starting chart begins controlling the process without the need for preliminary observations, an advantage when production is slow or when the cost of early out-of-control production is high. Furthermore, the use of estimated parameters substantially degrades the expected performance of conventional charts, a problem avoided by the proposed chart. The self-starting chart uses the deviation of each observation vector from the average of all previous observations. These deviations, or innovations, can be plotted on a T2 control chart or accumulated in a multivariate EWMA (MEWMA) chart. The run-length performance is evaluated for step shifts occurring at various points, and the MEWMA charts a...