Date: 201712
Local time of day: 1201-1800
Location: TEB.Airport, NJ
Flight conditions: VMC
Light: Daylight
Aircraft: Challenger 350
Operator: Fractional
Operating under: Part 91
Flight plan: IFR
Mission: Ferry / Re-Positioning
Flight phase: Descent
Airspace: Class E N90
ATC / advisory: TRACON N90
Aircraft component: Autoflight System
Component problem: Malfunctioning
Reporter organization: Fractional
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Human-Machine Interface
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Undershoot; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew FLC Overrode Automation; Flight Crew Overcame Equipment Problem
Contributing factors: Aircraft; Human Factors
Primary problem: Aircraft

Narrative: After crossing LVZ at FL240 per ATC instructions; we were given a crossing restriction to cross MUGZY at 6000 ft. We set 6000 in the altitude alerter; programmed the FMS; and activated VNAV. The VNAV carot appeared; Aircraft started to descend from the TOD (Top of Descent) at around 2000 fpm; then the VNAV carrot dropped to the bottom of the window; VSI cue dropped to 4000 fpm so went to VS and put the VSI in the cue at 4000 fpm. Knowing that I had to slow at 10;000 ft; I increased descent manually to about 5400 fpm. Automation indicated we would be at 6000; well before MUGZY. About 12 miles before MUGZY; ATC asked if we were going to make the crossing; We looked at the VSI and it was right on the cue to make the crossing; and the 'Carot' in the MFD displayed that we would; so PF replied 'Yes.' About a minute later ATC asked how far we were from MUGZY. DME indicated only 5.5 miles from MUGZY and we were still above 10000 ft. VSI cue was still showing us on target but that's when we realized we would miss the restriction. Had we had a reliable indication sooner; we could and would have just asked for vectors off course. We crossed MUGZY around 10400ft. ATC then issued a new clearance to just cross STW at 6000 ft.The auto flight system then failed to properly capture the ILS LOC and glideslope at TEB. It captured the localizer too soon and tried to parallel it. It then pitched up about 12 degrees and started a left turn in a 20 degree bank and crossed the LOC. As we were at about 2700 ft; descending from 3000 to 2000 per ATC; and were below the glide slope; I suspect it detected the GS above us and erroneously pitched up to catch it. I couldn't wait any longer to find out and just disconnected the automation and hand flew the rest of the approach. It appeared that the flight director returned to normal for the last 1000 feet of the approach. After landing; we wrote up the automation and consulted maintenance; which resulted in grounding the airplane. Maintenance suspected that the malfunction might be related to a previous problem.Try to always back up automation with old school math; if possible. Watch automation continuously as it apparently cannot be trusted; even to let you know when it's broke or confused by displaying an error message. We all know this; but it still manages to occasionally bite us. All said; learn from the experience.


Second narrative: [Report narrative contained no additional information.]


Synopsis: CL35 flight crew reported a malfunctioning FMS resulted in a missed crossing restriction and failure to properly capture the ILS localizer and glideslope.