  High-precision experiments have been done to test the Pauli exclusion
principle (PEP) for electrons by searching for anomalous $K$-series X-rays from
a Cu target supplied with electric current. With the highest sensitivity, the
VIP (VIolation of Pauli Exclusion Principle) experiment set an upper limit at
the level of $10^{-29}$ for the probability that an external electron captured
by a Cu atom can make the transition from the 2$p$ state to a 1$s$ state
already occupied by two electrons. In a follow-up experiment at Gran Sasso, we
aim to increase the sensitivity by two orders of magnitude. We show proofs that
the proposed improvement factor is realistic based on the results from recent
performance tests of the detectors we did at Laboratori Nazionali di Frascati
(LNF).
