  The method of quasi-optimal weights is applied to constructing
(quasi-)optimal criteria for various anomalous contributions in experimental
spectra. Anomalies in the spectra could indicate physics beyond the Standard
Model (additional interactions and neutrino flavours, Lorenz violation etc.).
In particular the cumulative tritium $\beta$-decay spectrum (for instance, in
Troitsk-$\nu$-mass, Mainz Neutrino Mass and KATRIN experiments) is analysed
using the derived special criteria. Using the power functions we show that the
derived quasi-optimal criteria are efficient statistical instruments for
detecting the anomalous contributions in the spectra.
