Flight Crew Air Transport Pilot (ATP)
Human-Machine Interface; Training / Qualification
Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Chart Or Publication; Human Factors; Procedure
60 miles southwest of RIDGY on the KORRY 3 arrival; ATC issued a crossing restriction; 'cross RIDGY at FL270.' When selecting the KORRY 3 out of the FMS; RIDGY has an assigned crossing altitude of at or above FL270. The pilot flying selected 27;000 [feet] in the altitude alerter and then selected VNAV. Both of us thought the FMS was programed correctly. ATC informed us about 15 miles from RIDGY that we were high and issued us a clearance to descend to FL240.  We immediately started a descent and crossed RIDGY 8;000 to 7;000 feet high. The FMS never started the descent due to the fact that RIDGY was programmed to cross at or above FL270. The proper altitude programming in the FMS at RIDGY should have been cross RIDGY AT FL270.  When selecting STARS out of the box; make sure the waypoint doesn't have a pre-assigned above or below designation.
Narrative contains no addtional information.
Cessna jet flight crew missed an ATC assigned crossing altitude by relying on an FMS programmed restriction which was 'at or above' rather than 'at' the crossing altitude.