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.

Extended control charts - Pdf manual

Task: Monitoring the process of pressing tablets in pharmacy plant

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 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.