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Unformatted text preview: MULTIVA RIATE CONTROL CHARTS A Multivariate Chart is a control chart for variables data. Multivariate Charts are used to detect shifts in the mean or the relationship (covariance) between several related parameters. Several charts are available for Multivariate analysis: • The T2 control chart, based upon Hotelling's T2 statistic, is used to detect shifts in the process. Instead of using the raw Process Variables, the T2 statistic is calculated for the process' Principal Components, which are linear combinations of the Process Variables. While the Process Variables may be correlated with one another, the Principal Components are defined such that they are orthogonal, or independent, of one another, which is necessary for the analysis. • The Squared Prediction Error (SPE) chart may also be used to detect shifts. The SPE is based on the error between the raw data and a fitted PCA (Principal Component Analysis) model (a prediction) to that data. • Contribution Charts are available for determining the Process Variables' contributions to either the Principal Component (Score Contributions) or the SPE (Error Contributions) for a given sample. This is particularly useful for determining the Process Variable that is responsible for process shifts. • Loading Charts provide an indication of the relative contribution of each Process Variable towards a given Principal Component for all groups in the analysis. Some restrictions apply to these analyses: • The process variables are restricted to a subgroups of size one. • No provision is made for missing data. If a sample row has an empty cell, an error message is provided, requiring that either the affected variable or the affected sample be dropped from the analysis. • This implementation specifically excludes PLS (Partial Least Squares) analyses, where the samples for the process variables are associated with quality parameters. Cuándo utilizar un gráfico multivariado When to Use a Multivariate Chart A Multivariate Analysis (MVA) may be useful in SPC whenever there is more than one process variable. MVA usually becomes useful when the effect of multiple parameters is not independent or when some parameters are partial or complete measures of some other parameters (correlation). In some cases the true source of variation may not be recognized or may not be measurable. For example, Pressure and Volumetric Flow may be the process parameters being controlled, but Temperature at some point in the process may influence both; the common parameter affecting the process might be Mass Flow. An essential point is that almost all processes are multivariate but MVA is often not...
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