Date: 201908
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Aircraft: B757-200
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Climb
Airspace: Class B ZZZ
ATC / advisory: Center ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Time Pressure; Workload; Human-Machine Interface; Communication Breakdown; Fatigue
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Contributing factors: Aircraft; Human Factors
Primary problem: Aircraft

Narrative: Flying from ZZZ I had programmed the FMC to be on the ZZZZZ arrival landing to the west. Winds in paperwork showed all winds out of west. After takeoff; we were cleared direct to ZZZZZ1 intersection. Enroute to ZZZZZ1 we got the ATIS; landing east. As I changed the runway in the FMC to 10; the Controller instructed us to decent via the ZZZZZ landing east. I selected 5;000 in MCP and noticed that the entire arrival had dropped out of the box. We alerted ATC that the arrival was dumped and he assigned 12;000 feet and present heading. When we finally got [to] ZZZZZ 10 selected in the box we let ATC know and he said to continue direct ZZZZZ2 and decent via the ZZZZZ. I selected 5;000 [feet] in altitude selector and started down. Passing through 8;900 feet; the Controller asked us to level at 10;000 [feet] due to terrain. I believe that in the rush of this flight and mix up; I never saw the aircraft go back into VNAV path and most likely stayed in VNAV speed to cross at 5;000 [feet]. We stopped descent and leveled back at 10;000 feet. We were vectored for Runway 10L and landed without incident. Factors that contributed to event/concern [were] my own fatigue; time pressures; interruptions/distractions; high workload/task saturation; problems with automation; [and] lack of assertiveness.


Second narrative: Planning for ZZZ1 landing [Runway] 28; the FMC was set up for our rout to ZZZZZ1. After takeoff at ZZZ we were cleared direct to ZZZZZ1 and climbed to our final altitude of 19;000 [feet]. Enroute; I obtained and alerted Captain of the ATIS; and nearing ZZZZZ1; she changed the FMC to Runway 10L. At the same time; the Controller cleared us to descend via the ZZZZZ Arrival landing east; Captain set 5;000 in the MCP; final altitude on the arrival. At ZZZZZ1; noticed that the entire arrival has dropped out of the FMC and the airplane was not navigating in LNAV to ZZZZZ2 as the next point; but we turned the airplane to head to ZZZZZ2 and she alerted ATC that the arrival had dropped from the FMC. ATC assigned present heading and 12;000 [feet]; which was immediately set into the MCP. With Captain flying the airplane and operating the FMC; I was requested to put the arrival back into the FMC; ZZZZZ STAR; landing [Runway] 10L at ZZZ1. We let ATC know that we had the arrival set-up and he cleared us; again; to descend via and continue direct ZZZZZ2. Captain selected LNAV and put 5;000 in the MCP. ZZZZZ2 was displayed in the FMC and in map mode as '11000A'. We continued and began running the approach checklist for our approach into ZZZ1. ATC alerted us to level at 10;000 [feet] due to terrain. We had passed through 10;000 [feet] by this time and stopped descending around 9;000 [feet]. In reviewing the arrival; the highest obstacle in the area is a peak at 8;334 [feet] approximately 10 miles to the east of the route and ZZZZZ2. It was clear below 25;000 feet at the time; with 10 miles visibility. Captain maintained positive control of the aircraft and quickly corrected; leveling at 10;000 [feet] as requested. I believe that the airplane probably stayed in or went back into VNAV speed instead of VNAV path; causing the airplane to continue the descent instead of leveling to cross ZZZZZ2 at 11;000 [feet]. With both crew task saturated during this very short flight; especially following the issue with the FMC and arrival; we failed to notice this occurrence. Following this; we were vectored for the approach for RWY 10L and landed without incident at ZZZ1. Factors that contributed to event/concern [were] my own fatigue; time pressures; interruptions/distractions; [and] high workload/task saturation.


Synopsis: B757 flight crew reported low altitude alert by ATC when aircraft descended due to incorrect automation management.