A320
Flight Crew Air Transport Pilot (ATP)
Human-Machine Interface; Confusion
Aircraft Equipment Problem Critical; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Human Factors; Chart Or Publication; Aircraft; Procedure
We were inbound to ZZZ at a cruise altitude of FL220 and were cleared to descend via the ZZZZZ TWO; south transition. We had already passed ZZZZZ1; which is the first fix on the ZZZZZ TWO and has a crossing restriction of FL230. The next fix is ZZZZZ2 which has a crossing restriction of FL220. We were between ZZZZZ1 and ZZZZZ2 at FL220 and selected 6;000 for the south transition and started a managed descent.I was anticipating the FMS would have a constraint of 220 until ZZZZZ2 but the FMS started descending before ZZZZZ2. We were both discussing the ZZZZZ  charting and we noticed the descent at about FL212 at which point we climbed back up to 220 just about the time that we crossed ZZZZZ2. Center reported no traffic conflicts but did provide a landline number to call which the Captain did after landing. He also spoke with Approach.Both the Captain and I have been on the Airbus for many years so we are well familiar with the aircraft's systems and behaviors. Neither of us can figure out why there wasn't a constraint at ZZZZZ2 for FL220. Perhaps it was because we 'cleared via' the ZZZZZ TWO while at a cruise altitude 'below' the initial [restricted] fix (ZZZZZ1)? Neither of us could recall starting a 'Descend Via' STAR at such a low altitude before so perhaps that is an issue with the FMS. If it can be determined that the FMS cannot accept starting a 'Descend Via' STAR at an altitude below the initial one then there needs to be a software modification to allow it to do so or Airbus pilots will have to manually perform the descent.
I selected 6;000 FT for the lowest altitude on the arrival and selected managed descent past ZZZZZ1 and prior to ZZZZZ2 Intersections.Upon reverifying the altitude constraints it was noted that that ZZZZZ2 constraint of FL220 had been deleted.
The flight crew of an A320 was cleared via the ZZZZZ RNAV STAR while in cruise flight at a Flight Level (FL220) below that of the initial altitude restriction on the STAR (FL230). When Managed Descent was engaged the FMGC initiated a descent from FL220 despite not yet crossing the next waypoint; which requires crossing at FL220. When advised by ATC the crew noted that the FL220 restriction had not been processed by the FMGC.