Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 5
Situational Awareness; Distraction; Communication Breakdown
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance
Human Factors
Aircraft X was given a heading of 110 to join the localizer; maintain 2;000 feet until established and cleared for the ILS 13R approach at HOU. The pilot read back 'one one thousand; maintain 2;000 feet till established on the ILS 13 cleared ILS 13.' I remember him saying the one one thousand which of course was wrong; but I was fairly certain he meant 110 heading. He did state the altitude to maintain correctly so I did not make a new transmission to get a different read back. I switched him to HOU Tower when he was at 019. Since he was the last aircraft for a few minutes; I remember taking a drink of my water and standing up to stretch my legs. The LA (Low Altitude) alert sounded and I quickly called HOU Tower for them to issue the MSA alert.  The aircraft had descended to 010 on the localizer 1.5 miles from the FAF.  The crossing altitude for the FAF is 020 and the MVA in the area is 020 and the MVA in the area is 2;000 feet. I did not notice his quick descent since the few seconds had elapsed from when I switched him to the Tower.Maintain a steady scan of all aircraft at all times until they are safely outside the area of my responsibility. Make sure every read back is 100% accurate; 100% of the time.
Houston TRACON Controller reported a partially incorrect readback which lead to an aircraft descending below the MSA in the area.