ACFT EQUIP PROB -- ACR ON TKOF LOSES THE CAP OF ONE OF THE NOSE GEAR TIRES. THAT CAP STRIKES THE ELECTRONIC COMPARTMENT IN THE BELLY OF THE ACFT CAUSING A NUMBER OF ELECTRONIC SYS TO MALFUNCTION OR SHUTDOWN.

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PRIOR TO AND DURING TKOF ROTATION. AFTER SEPARATION TREAD IMPACTED FUSELAGE APPROX 2 FT AFT OF THE E&E COMPARTMENT HATCH. IMPACT SHOCK CAUSED LOSS OF BOTH ATTITUDE HDG REF SYS GYRO SYS; FAILURE OF BOTH ATTITUDE INDICATORS; BOTH HDG INDICATORS; BOTH FLT DIRECTORS. CONTINUED FLT ON STANDBY HDG AND ATTITUDE. UNABLE TO RESTORE NORMAL FLT INSTS. RETURNED TO PHX. LANDED AT 140000 LBS (10000 LBS ABOVE MAX LNDG WT). FILED APPROPRIATE RPTS WITH COMPANY AND FAA. NO PRIOR INDICATION OF IMPENDING TIRE FAILURE. THE SMELL OF BURNING RUBBER IN COCKPIT AFTER LIFT-OFF SUGGESTS POSSIBLE INGESTION OF TIRE FRAGMENTS BY ENG. NO KNOWN ENG DAMAGE. THE LNDG WAS UNEVENTFUL AFTER A FLYBY; RPT BY TWR PERSONNEL THAT 'BOTH NOSE TIRES APPEAR SHREDDED' ACTUALLY; LEFT NOSE TIRE INTACT; CARCASS OF R TIRE REMAINED FULLY INFLATED AFTER LOSS OF ENTIRE TREAD. AFTER ARRIVING AT GATE; BOTH ATTITUDE HDG REF SYS RE- ALIGNED AND OPERATED NORMALLY. SEE ENCLOSED COMPANY BULLETIN REGARDING THIS INCIDENT. BELIEVE COMPANY IS EXPERIENCING HIGH RATE OF TIRE FAILURES. (EG; ABORTED TKOF; ENG DAMAGE AFTER MAIN GEAR TIRE FAILURE ON AN MD80 ACFT OF JUN/FRI/95 BWI ARPT).