What was found
DURING FL 350 AND AS CRUISE ALTITUDE, THE NR 1 ENGINE OIL PRESSURE LIGHT ILLUMINATED AND THE EGT BECAME ERRATIC. PERFORM CHECKLIST, SHUT DOWN ENGINE AT 0819Z, OIL PRESSURE READING 45 PSI. ON LANDING SMELLED BURNING SMELL IN COCKPIT. LANDED WITHOUT INCIDENT. INSPECTION OF THE NR 1 ENGINE REFLECTS REVEALED PYLON HARNESS BURNS NEAR THE ANTI-ICE MANIFOLD ASSY. CAUSE WAS DUE TO THE FWD ANTI-ICE COUPLING ASSY (P/N-735138) LOOSE, DUE TO HAVING A SHEARED BOLT (361615). BOLT, WASHER AND NUT WERE REPLACED WITH NEW PARTS, AND TORQUE IAW STANDARD PRACTICES. REMOVED AND REPLACED DAMAGE WIRING. PERFORMED ENGINE RUN TEST AND PNEUMATIC SYSTEM CHECKS AND FOUND SATISFACTORY.