Date: 201510
Local time of day: 1201-1800
Location: ZLA.ARTCC, CA
Flight conditions: Marginal
Weather elements / visibility: Turbulence
Light: Daylight
Aircraft: Embraer Phenom 100
Operator: Fractional
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class C ZLA
ATC / advisory: Center ZLA
Aircraft component: Pressurization System
Component problem: Malfunctioning
Reporter organization: Fractional
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Commercial
Human factors: Distraction; Communication Breakdown; Troubleshooting
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Contributing factors: Aircraft; Human Factors
Primary problem: Human Factors

Narrative: During our arrival into the Southern California area on the KAYOH 5 arrival we were assigned to deviate off the arrival for weather.  We were then assigned to cross a fix at so many miles at an altitude assigned by ATC. (I don't want to list what the specific fix and altitude were because I cannot remember with 100% accuracy due to the time between knowledge of possible deviation and actual occurrence). Due to the aircraft's previous Bleed 2 failures that had been occurring during decent to low altitudes; (and had been written up on a previous leg) I missed the initial PNF ATC clearance readback while I was monitoring the aircrafts systems. (The aircraft was subsequently written upon our arrival to SNA for just that problem and a full CMC download was required). I then asked the PNF what the instructions were and told him I had missed them because I had been checking the synoptic page; He told me and I set the Altitude the PNF heard; and repeated to me; into the [flight computer]; I then set the crossing restriction into the flight plan's ATK feature and initiated a VNAV descent via the autopilot. That controller then handed us off to the next controller. During the check on with the new controller I heard the PNF read back the altitude we had set in the [flight computer] and the crossing restriction and heard NO correction from that controller.During the descent it became apparent to me that due to the terrain and geography of the area; the assigned altitude seemed excessively low; and the situation raised a red flag in my head. As a precaution I immediately initiated a level off and began a climb while simultaneously asking the PNF to verify that the assigned altitude was correct for this area.  The controller told us 'negative' and to climb and maintain 13;000 ft.  Which we immediately did. At no time did the controller tell us we were below our assigned altitude nor did they issue any other warnings. It was only by PIC action that a correction took place. I took the comms to query ATC as to what had happened and the controlled seemed completely unsure. I believe he asked what we had been assigned and said he would check with the previous controller. When he finally came back to us he simply proceeded to hand us off to the next controller; but before switching off I asked him if this was something I needed to worry about; (a pilot deviation) or if I could be expecting a phone number? He said No; and I took that to mean that the error had been on ATCs end and would we not need to protect ourselves with a NASA report.  At no time were we ever told we had deviated from an assigned altitude or clearance; and because the controller told us we shouldn't need to worry about a deviation; neither myself nor my co-pilot filled out a NASA report. It is due to that reason why neither of us can recollect with 100% accuracy; (on our end) what altitudes were involved. The time between the incident and time we were made aware of a possible deviation made that impossible. We do recall during the initial check on/read-back with that final controller; that the altitude and clearance was what we had in put into the FMS and AFCS respectively.I believe my first error in this event took place when I allowed myself to become distracted by the aircrafts previous CAS messages during low altitude operations and while monitoring the systems in an attempt to diagnose them; I missed the Initial ATC instructions. The other error was not asking the PNF to reconfirm the initial clearance with ATC since I had not heard it directly.  I will now be more vigilant in both areas and also will fill out a NASA form even if I am led to believe; or do not believe a deviation or safety issued but could still be possible.




Synopsis: Phenom 100 Captain reports not hearing a descent clearance while troubleshooting a pressurization problem and asked the First Officer to repeat it; which he does; but apparently incorrectly. When raising terrain makes the clearance seem obviously wrong; ATC is queried and the crew is told to climb to 13;000 feet.