It is frequently required to control two or more quality characteristics simultaneously during statistical process quality control. So the multivariate quality control exists widely. When the statistical process quality control is performed for multi-characteristics in the course of product manufacturing, joint control of multi-characteristics cannot be replaced by separate control of each characteristic, because their control fields are different. Therefore, it is essential to study the multivariate control charts.For multivariate statistical process the usually recommended procedure is multivariate control chart, especially T 2control chart and EWMA chart. In the retrospective phase the common covariance matrix is always unknown and several approximate distributions of statistic based on different estimators are compared. Calculation methods for upper control limit of different T 2 charts with different sample size m and quality dimensions p are proposed.An improved MEWMA chart based on successive differences estimator S 2 is established. With different smoothing factor r and non-centrality parameterλ, the signal probabilities and ARL (Average run length) of two MEWMA charts are compared when two types of shifts in mean vector occur. A case study based on simulation is presented to show the different properties of several T 2 and MEWMA charts when common covariance matrix is estimated.
|