Hull resiliency was a measurement of how well a hull could withstand damage.
In 2370, inside the USS Enterprise-D's shuttlebay, Lieutenant Commander Geordi La Forge and Ensign Taurik evaluated the hull resiliency of the shuttlecraft Curie by firing upon it with a phaser rifle. Taurik was a little puzzled that they were intentionally damaging the shuttlecraft. La Forge responded that Starfleet required periodic testing, which Taurik was unfamiliar with. Taurik then offered to reconfigure the phaser to fire a low-intensity burst that would not harm the shuttle's hull and the test procedure would not be affected, but this was rejected. La Forge then requested another burst on the port side of the vessel for about four seconds. Taurik intuited that it wasn't a real test, but rather the shuttle was meant to appear that it had fled from an attack while engaging in evasive maneuvers. (TNG: "Lower Decks")