Introduction to Multivariate SPC

A bunch of Advanced Techniques used for the monitoring and controlling of the operating performance of batch and continuous processes is known as Multivariate SPC (Multivariate Statistical Process Control Chart)

The most important benefit of multivariate SPC techniques is it reduces the information contained within all the process variables down to two or three composite metrics by implementing statistical modeling technique. These composite metrics can be monitored easily in real-time in order to benchmark the efficiency of the process and determine potential problems, thereby providing a platform for continuous improvements in the operation process.

As the complexity of products and processes increases and the amount of data grows, traditional unilabiate SPC and analytical tools may not be competent enough to provide the insight required by the engineers for their routine activities. Instead, they will need to understand and control processes which are listed by multiple variables, where the relations between the variables are not only complex but also often unknown. The most challenging aspect of this is to make statistical analysis of multiple interdependent variables, more efficient, intuitive, understandable and reliable as unilabiate SPC and analytics.


Multivariate Charts are control charts for variables data. Multivariate Statistical Process Control Charts are used to detect shifts in the relationship (covariance) between several related parameters.

Various different control charts for variables data are available for Multivariate Statistical Process Control analysis:

T2 control charts for variables data, based upon the Hoteling T2 statistic, are used for Analysing shifts in the process. In Place of using the raw Process Variables, the T2 statistic is calculated for The main Components of the process, which are linear combinations of the Process Variables. While the Process Variables may be correlated with one another, the Principal Components are defined in a way so that they are independent, of one another, as required for the analysis.

The Squared Prediction Error (SPE) chart can 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 to as a certain the contributions of the Process Variables 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 give an indication of the relative contribution of each Process Variable towards a given Principal Component for all groups in the analysis.

Few restrictions are an application to these Multivariate Statistical Process Control analyses:

• The process variables are restricted to a subgroup of size one.

• Provision for missing data is not available. If a sample row has an empty cell, this will throw an error message, requiring that either the affected variable/sample should be dropped from the analysis.

• This process specifically excludes PLS (Partial Least Squares) analyses, where the samples for the process variables are linked with quality parameters.

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