Combined synthetic and |S| chart for monitoring process dispersion

ABSTRACT

This article proposes a multivariate control chart, the syn-|S| chart, which comprises a standard |S| subchart and a multivariate synthetic sample generalized variance |S| (synthetic |S|) subchart, for detecting shifts in the covariance matrix of a multivariate normally distributed process. A procedure for the optimal design of the syn-|S| chart by minimizing the average extra quadratic loss is provided. The syn-|S| chart has better overall performance compared to the synthetic |S| chart and the standard |S| chart, based on the zero-state and steady-state modes. An example is given to illustrate the operation of the synthetic |S| chart.

KEYWORDS:

• Average run length
• Multivariate chart
• Sample generalized variance
• Synthetic chart

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30
• 90C90