Equipment accuracy as approved for flying SIDs/STARs:
GPS or dual DME - Type A Procedure: +/- 2nm
GPS or dual DME & IRU - Type B +/- 1nm
Both criteria must be adhered to 95% of the time or better. A bust would be up to the person on the box.
Have a look at the FAA's AC 90-100 (Advisory Circular) and for Eurocontrol AC 90-96A for more. The basics are covered in 90-94.