In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewharttype control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial least squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.

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The coefficient of variation (CV) is a quality characteristic that has several applications in applied statistics and is receiving increasing attention in quality control. Few papers have proposed control charts that monitor this normalized measure of dispersion. In this paper, an adaptive Shewhart control chart implementing a variable sampling interval (VSI) strategy is proposed to monitor the CV. Tables are provided for the statistical properties of the VSI CV chart, and a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV. An example illustrates the use of these charts on real data gathered from a casting process.Castagliola et al. 5 suggested a new method to monitor the CV by means of two one-sided EWMA charts of the CV squared. The performance investigation requires for this chart an extensive computational analysis based on a Markov chain approach (whereas the Hong et al. 4 approach is only based on simulation). A numerical analysis demonstrated that the control chart proposed by Castagliola et al. 5 almost always yielded smaller ARL values than the control chart proposed by Hong et al., 4 even if this statistical outperformance is often rather small.Very recently, Calzada and Scariano 6 suggested a synthetic control chart (denoted SynCV) for monitoring the CV. The results showed (see Table 8 in Calzada and Scariano 6 ) that the out-of-control ARLs obtained for the SynCV chart are obviously smaller than the ones for the CV chart of Kang et al., 3 but the former are generally larger than the out-of-control ARLs obtained for the EWMA-CV 2 chart of Castagliola et al. 5 as long as the increasing shift in the CV is not too large. Contrary to Castagliola et al., 5 in which the authors investigated both the CV increasing and decreasing cases, Calzada and Scariano 6 only provided results concerning the CV increasing case.Shewhart-type control charts have been extensively adopted with the advantage of their easy implementation. They provide good performance in detecting large changes in the process mean. However, they may take a longer time to detect small and moderate shifts. Classical alternatives to overcome this problem are using more advanced-type control charts such as the supplementary run rules chart, the synthetic chart, the cumulative sum (CUSUM) control chart, or the EWMA control chart and/or using adaptative strategies such as the variable sampling interval (VSI) charts and the variable sample size (VSS) charts. A very comprehensive survey about the design of adaptive charts was presented by Tagaras. 7 It covers all kinds of adaptive charts that use variable sample sizes, variable sampling intervals, and variable control limit coefficients, as well as different combinations of adaptive design parameters.In the sampling interval control charts, the sampling interval h is allowed to vary as a function of the prior sample position. The sampling interval chart uses control and warning limits, which divide the chart into three regions: the safe region, the warning region, and the out...

International audienc

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