Self-Starting Multivariate Exponentially Weighted Moving Average Control Charting

Summary: [This abstract is based on the authors’ abstract.] Designing control charts involves using in-control process parameters that are presumed to be known exactly, but in most industrial applications, the parameters are unknown and are estimated in a special phase I calibration exercise. This adds a random element to the run length performance and may harm the performance of the chart. Existing univariate self-starting methods can begin the control of the process right after startup without the preliminary large phase I sample. This study develops a multivariate equivalent by transforming the process readings into a stream of vectors following an exact known-parameter distribution. This stream of vectors may be used to construct any multivariate control chart. The multivariate exponentially weighted moving average chart constructed to illustrate the method will have the same in-control properties as when the process mean and covariance matrix were known exactly.