Control limits should not depend on a test set

[codepictor]

Hi there!

First of all, thank you for making a great visualization of applying Hotelling's T2 to analyzing multivariate time series data! It really helps understand how it works.

Take a look at the following line:

hotelling/hotelling/plots.py

Line 147 in ac6ef7d

lcl, cl, ucl = control_interval(m, n, f, phase=phase, alpha=alpha)

.

It seems that the control limits (lcl, cl, ucl) depend on the x size. It also happens when the parameter 'phase' is set to 2. So, if you change the x size, these control limits will be recalculated. However, the second phase is used to maintain control with future values, that is to compare new values of the charting T2 statistic with these three limits. By the start of the phase 2 these limits should have been established, and they should remain constant during the second phase.

We can also take a look at the example consisting of the 14 data observations:
https://github.com/dionresearch/hotelling/blob/master/notebooks/hotelling_control_chart_example.ipynb.
The correct UCL seems to be equal 31.33 (in the notebook it is equal to 28.872).

Would be really glad to see any feedback. Thanks!