Given a flight's tail-number, is there a way to search for the on-time statistics of that plane?
So far I've only found ways to search for on-time statistics per route.
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To be quite honest I think you are barking up the wrong tree but you can try and use a suggestion from Airliners.net thread on maintenance records.
It may be possible to receive at least some information on aircraft maintenance from Plane Fax but as was suggested these may have be a matter of public record. But if you feel like spending $99 for a report let us know if this was useful.
Though you would have a very difficult time proving that a plane that arrived to an airport with no issues reported have had problems severe enough with that particular piece and that airline knew about it but didn't fix.
But good luck.
http://www.flightstats.com/go/FlightRating/flightRatingByRoute.do I think thats what you're looking for