# Probability and Statistics Seminar

### 07/03/2017, 11:00 — 12:00 — Room P3.10, Mathematics Building

Manuel Cabral Morais, *DM-Instituto Superior Técnico; CEMAT*

### Comparison of joint schemes for multivariate normal i.i.d. output

The performance of a product frequently relies on more than one quality characteristic. In such a setting, joint control schemes are used to determine whether or not we are in the presence of unfavorable disruptions in the location and spread of a vector of quality characteristics. A common joint scheme for multivariate output comprises two constituent control charts: one for the mean vector based on a weighted Mahalanobis distance between the vector of sample means and the target mean vector; another one for the covariance matrix depending on the ratio between the determinants of the sample covariance matrix and the target covariance matrix. Since we are well aware that there are plenty of quality control practitioners who are still reluctant to use sophisticated control statistics, this paper tackles Shewhart-type charts for the location and spread based on a few pairs of control statistics that depend on the nominal mean vector and covariance matrix. We recall or derive the joint probability density functions of these pairs of control statistics in order to investigate the impact on the ability of the associated joint schemes to detect shifts in the process mean vector or covariance matrix for various out-of-control scenarios.

Joint work with Wolfgang Schmid, Patrícia Ferreira Ramos, Taras Lazariv, António Pacheco.