  The VIolation of Pauli exclusion principle -2 experiment, or VIP-2
experiment, at the Laboratori Nazionali del Gran Sasso searches for x-rays from
copper atomic transition that are prohibited by the Pauli Exclusion Principle.
Candidate direct violation events come from the transition of a $2p$ electron
to the ground state that is already occupied by two electrons. From the first
data taking campaign in 2016 of VIP-2 experiment, we determined a best upper
limit of 3.4 $\times$ 10$^{-29}$ for the probability that such a violation
exists. Significant improvement in the control of the experimental systematics
was also achieved, although not explicitly reflected in the improved upper
limit. By introducing a simultaneous spectral fit of the signal and background
data in the analysis, we succeeded in taking into account systematic errors
that could not be evaluated previously in this type of measurements.
