A Self-Starting Control Chart for Multivariate Individual Observations

Abstract

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 are shown to outperform T2 charts in rapidly detecting process changes. We show that for self-starting charts, performance comparisons based on the average run length can be misleading and introduce a new performance criterion.