Tests for special causes with multivariate autocorrelated data

Runs tests for special causes are used routinely with Shewhart quality-control charts that are based on independent and identically distributed univariate processes. Recently, researchers have proposed the use of alternative, time-series-based statistical models for constructing control charts that are valid for autocorrelated processes. Monte Carlo simulation is used here to examine the effects of incorrectly assuming serial independence and using the runs tests for special causes on data generated by autocorrelated multivariate processes. The results have implications for developing and using statistical process-control techniques in practice.