B737-700 CAPT RPTS AIRSPEED AND ALTIMETER ANOMALIES AT FL380; EEC'S GO TO ALTERNATE MODE. CYCLING PITOT HEAT SWITCH SEEMS TO SOLVE THE PROB.

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IN CRUISE FLT THE CAPT'S AIRSPEED STARTED TO SLOWLY DECREASE. FO AND STBY AGREED; TRIM WHEEL WAS STABLE; SO WE AGREED WE HAD A PROBLEM ON THE CAPT SIDE. THE CAPT'S ALTIMETER STARTED SLOW CLB. MASTER CAUTION CAME ON. I LOOKED ON OVERHEAD AND BOTH EEC IN ALT MODE. ATC CALLED AND SAID YOU ARE SHOWING 300 FT HIGH. I TOLD HIM WE HAD A COMPUTER FAILURE AND WOULD LIKE A BLOCK FL380-FL390 AND HE GRANTED IT. I THEN SWITCHED FROM #1 TRANSPONDER TO #2 SO IT WOULD AGREE WITH THE WORKING INSTRUMENTS. CTR SAID WE WERE SHOWING RIGHT ON FL380. WHILE FO FLEW THE ACFT I CHECKED ALL CIRCUIT BREAKERS AND NONE WERE OUT. I THEN GRABBED THE QRH AND COMPLIED WITH THE NON-NORMAL CHECKLIST FOR THE EEC'S. THEN THE NON-NORMAL FOR UNRELIABLE AIRSPEED AND UNRELIABLE ALTITUDE. I ASKED THE FO IF HE WOULD BE COMFORTABLE IF I RECYCLED THE PITOT HEAT. HE SAID YES; AND I DID. CAPT'S INSTRUMENTS CAME BACK SLOWLY (2 MINS APPROX). ALL INSTRUMENTS AGREED AND CDU AIRSPEED DISAGREEMENT NOTE CLEARED. THE LAST THING WE HAD TO DECIDE WAS STAY IN OR OUT OF RVSM. EVERYTHING WAS WORKING NOW EXCEPT WE HAD LEFT THE EEC'S IN THE ALT POSITION AS PER QRH. I FELT THE ENGINES WERE STABLE AND THOUGHT IT WAS NOW SAFE TO GIVE UP 10000 FT AND GO TO FL280 THE LAST HOUR OF THE FLT (PLENTY OF FUEL). WE NOTIFIED DISPATCH AND MAINT ENRTE AND WROTE IT UP. WE HAD BEEN IN A STEADY CIRRUS LAYER FOR ABOUT 45 MINS PRIOR TO THE EVENT. I THINK IT WAS ABOUT -62; BUT I REALLY THINK IT WAS A STATIC PORT OR A PITOT PROB. I AM A BIG FAN OF HEATED STATIC PORTS. ALTHOUGH I AM ALSO NOT AN EXPERT IT COULD HAVE BEEN A COMPUTER. WE NEVER HAD A PITOT ANNUNCIATOR.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR WAS NOT AWARE OF THE MAINTENANCE PROCS REQUIRED TO RETURN THE ACFT TO SERVICE. THE EEC'S DO HAVE A PITOT STATIC INPUT THROUGH THE ADC'S SO THE TWO ANOMALIES WERE ALMOST CERTAINLY RELATED. THE FACT THAT THE PITOT STATIC PROBLEMS DISAPPEARED AFTER CYCLING THE PITOT HEAT SWITCH IS A STRONG INDICATION THAT PITOT HEAT WAS THE CULPRIT IN THIS INCIDENT. NO PITOT HEAT WARNINGS WERE EVER RECEIVED; EXCEPT WHEN THE SWITCH WAS CYCLED OFF.