Reynoldsno 1. "GPS Procedures have worked fine since introduced.."
That is a sweeping generalisation. Few pilots will admit officially to a cocked up GPS/NPA approach and as a result there is a huge gap in our knowledge of what could have gone wrong. Fine if the approach is conducted visually in daylight, but not fine if the stuff up's were IMC or night.
There have been two fatal accidents in Australia which claimed the lives of passengers and crews where either GPS defects or more likely mis-reading of the GPS/NPA instrument approach chart were suspected. This may have been due chart design with its accent on distance to various inbound waypoints rather than distance to the runway. In both accidents, low cloud and poor visibility were a factor. There is little doubt of the accuracy of GPS in tracking, but keeping above each stepped safe altitude is the weak link.