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.

KEY WORDS :

• Exponentially weighted
• Innovation
• MEWMA
• Probability integral transformation
• Q-chart
• Recursive residual
• Statistical quality control