| Control charts are one of the most powerful tools for monitoring a process. Univariate control charts are useful for monitoring processes that manufacture products with a single quality characteristic of interest. In many cases, products may be characterized by two or more quality characteristics that jointly determine the usefulness or the quality of the product. In many instances, these quality characteristics are correlated and, therefore, alternative multivariate control chart techniques are required to monitor the process that manufactures such products.; The performance of the multivariate control chart procedures that are currently being used in industry and that are being cited in the literature have been studied under the assumption that the underlying distribution of the process is multivariate normal. It is well known that in reality this assumption rarely holds. Our results indicate that the normal theory multivariate control charts perform poorly when departures from multivariate normality occur. Alternatives to the normal theory multivariate control charts are needed in case the assumption of multivariate normality fails to hold. One such alternative is based on the notion of data depths which leads to non-parametric multivariate control charts. However, our simulation studies indicate that the performances of the data depth multivariate control charts are poor under both multivariate normality and under departures from it.; We propose robust alternatives which are based on affine-invariant one-sample multivariate versions of the sign and sign-rank hypotheses tests. These hypotheses tests are used to construct multivariate Shewhart type and exponentially weighted moving average (EWMA) charts. Our simulation results indicate that the performance of the proposed charts are comparable to the performance of the normal theory and the data depth based multivariate control charts under the assumption of multivariate normality. On the other hand, the performance of the proposed charts are an improvement over the performance of the normal theory and the data depth based multivariate control charts under departures from multivariate normality. |
