Special Control Charts - Hotelling multivariate chart
Hotelling control chart is used when several correlated variables are controlled simultaneously. Within this module, the data are assumed to consist of individual (multivariate) data points, hence the chart is a multivariate analogue of the X-individual chart. Such data might be used in X-individual control charts for separate variables only if the variables are not correlated – their correlation coefficients should not be significant. Hotelling chart reduces the information about individual variables to one characteristic, namely distance from the (multivariate) mean computed with respect to the covariance matrix (Mahalanobis distance). The distance cannot be negative and respects interrelationships among different variables. The lower limit is always set to zero.

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Example

Task: Monitoring the process of pressing tablets in pharmacy plant

Data:
Weight Width Strength Hardness
122.4 12.10 2.45 1715
134.6 12.97 2.69 1728
127.7 12.41 2.38 1865
141.1 13.50 2.60 1830
140.1 13.43 2.46 1831
131.3 12.83 2.50 1792
130.1 12.66 3.08 1751
... ... ... ...

Hotelling multivariate chart

Output:
Hotelling Control Chart    
     
Task name : Pills  
Column name Target values Process mean
weight1 132.3565217 132.3107143
thickness1 12.85304348 12.82357143
strength1 2.920869565 2.911785714
hardness1 1769.608696 1766.5
     
Parameters of the chart :    
LCL : 0  
UCL : 16.42393612  

Hotelling chart for multidimensional data can find problems and unstabilities tha classical Shewhart chart cannot see, as Hotelling charts take into account also correlation structure of the process.

Hotelling multivariate chart