Yes, the fuel pump could be bad, or the in-tank sock filter on the pump could be restricting flow. You should check fuel pressure. The new fuel filter is probably not at fault.
Engine Running: 30-45 PSI
Key On Engine Off: 35-40 PSI
Run the engine at 2500 rpm for one minute and check whether fuel pressure remains in the above range. If the pressure is dropping when the engine warms up, diagnosis should focus on fuel system. Anything restricting fuel flow to the inlet of the pump will cause low fuel pressure.
Also, pull the vacuum line off the fuel pressure regulator and make sure there is no evidence of fuel in the vacuum line from the regulator's diaphragm leaking. Replace the regulator if there is any sign of leaking.
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It sounds like he is just guessing. Have the fuel pressure checked, or get a gauge and do it yourself. The fuel pressure regulator is easy to check.
The distributor could be tested with a scope to see if the Hall effect sensor inside is providing a good signal when the problem is occurring. I would not let him replace it unless he can prove it is faulty. The distributor is not typically a weak point, they last pretty well.
Look for a mechanic with a good reputation for fixing "driveability" problems. Often, the Ford dealers have good driveability techs. But there are also some good independent shops too. If it looks like the mechanic does mostly replacing instead of diagnosing, try to get a second opinion from one who is willing to diagnose, then repair. Keep an eye out for the use of good test equipment. Some shops specialize in things like replacing brakes and spark plugs. Other shops specialize in taking the time to dig in and find what's wrong with a car.
It is important to understand that the codes you are getting do not necessarily identify a certain component. The codes indicate excessive oxygen being detected in the exhaust stream. A misfiring cylinder can result in unburned oxygen going into the exhaust. Also, a malfunctioning air injection diverter valve can also cause oxygen to be pumped into the exhaust. Low fuel pressure can also be a cause. If the mixture is so lean that not all the oxygen burns, the leftover oxygen goes into the exhaust.
I pasted some of the pinpoint tests for the codes below, to give you an idea of the tests that can be done, and the types of faults that the tests look for.
H1 CHECK FOR FUEL DILUTED ENGINE OIL ___________________________________________________
Diagnostic HO2S Fault Trouble Orientation Definition Code (DTC) ____________________________________________________
172r right or rear system indicates lean 136r left or front 176c left or front ____________________________________________________
173r right or rear system indicates rich 137r left or front 177c left or front ____________________________________________________
144c right or rear no HO2S switch 139c left or front detected ____________________________________________________
171c right or rear adaptive fuel limit 175c left or front reached ____________________________________________________
NOTE:Due to the Tubular Exhaust Manifold configuration on the 4.9L inline 6-cylinder SFI (California) application, HO2S-2 is located in front of HO2S-1. A general rule is that HO2S-1 is always assigned to cylinder No. 1. Special attention must be given to HO2S location and DTCs on the 4.9L SFI (California) applications.
-- Fuel injectors.
-- Secondary Air Injection (AIR) system.
-- MAP sensor.
-- Electronic Ignition Coil Failure.
l Key off.
l Remove the PCV valve from the valve cover. Inspect both rocker cover hole and PCV for damage, sludge build up, blockage and movement of valve plunger. Service as necessary.
l Run Key On Engine Off (KOEO) and Key On Engine Running (KOER) Self-Tests.
l Address any Continuous Memory DTCs before servicing KOER DTCs.
NOTE:For a No Start, go directly to «H2».
l Are any of the above DTCs present in KOER Self-Test?
YesREINSTALL PCV valve. GO to «H2».
NoFor Continuous Memory DTCs 139, 144, 171, 176 or 177:GO to «H2» All Others:CHANGE engine oil and filter. REINSTALL PCV valve. DRIVE vehicle 5 miles/55 mph. RERUN «Quick Test».______________________________________________
H2 CHECK FUEL PRESSURE
WARNING:THE FUEL SYSTEM WILL REMAIN PRESSURIZED WHEN ENGINE IS NOT RUNNING. TO PREVENT INJURY OR FIRE USE CAUTION WHEN WORKING ON THE FUEL SYSTEM.
l Install fuel pressure gauge.
l Verify that manifold vacuum is connected to the fuel pressure regulator if applicable.
If engine will start:
l Start and run engine at idle. Note fuel pressure.
l Increase engine speed to 2500 rpms and maintain for one minute. Note fuel pressure.
l Refer to «Fuel Pressure Specification Table».
If engine will not start:
l Cycle the key off and on several times. Note fuel pressure.
l Is fuel pressure within specification for the engine being tested?
YesGO to «H3».
NoREFER to «Section 9A» for Fuel System Diagnostics.______________________________________________
H3 CHECK SYSTEM'S ABILITY TO HOLD FUEL PRESSURE
l Pressurize fuel system per step «H2».
l Visually look for fuel leaking at the injector O-ring, fuel pressure regulator, and the fuel lines to the fuel charging assembly. Service as necessary.
l Key on, engine off.
l Does fuel pressure remain at specification for 60 seconds?
YesFor No Starts:GO to «H4».For Service Codes or other Symptoms:MFI: GO to «H5».SFI: GO to «H6». (Your car is SFI- Sequential Fuel Injection)
NoREFER to «Section 9A» for Fuel System Diagnostics.________________________________________
H6 CYLINDER BALANCE DIAGNOSTIC TEST MODE (DTM) SFI ENGINES
The DTM switches each injector OFF and ON one at a time. Diagnostic Trouble Codes (DTC) correspond to the cylinder number (i.e., Service DTC 30 indicates a problem with cylinder No. 3, a DTC 90 indicates a pass.) The Cylinder Balance (DTM) is designed to aid in the detection of a weak or non-contributing cylinder. The Pinpoint Test Steps are designed to isolate only EEC related problems.
Refer to Quick Test Appendix, «Section 5A», for detailed information about Cylinder Balance (DTM).
l Run the Engine Running Self-Test.
l After the last repeated code, wait 5-10 seconds.
l "Goose" throttle lightly (not wide-open-throttle).
l Cylinder Balance (DTM) will be performed. Time of test is approximately 2-3 minutes.
NOTE:If KOER DTC 244 (for 2.0L Probe only) is output, Cylinder Balance DTM has been aborted, immediately go to Pinpoint Test Step «DR1».
l Are there any cylinder balance DTCs requiring service?
YesGO to «H8».
NoFor Symptoms: RETURN to «Section 2A».For DTCs 136, 172 and 176:GO to «H13».For DTCs 137, 173 and 177:GO to «H24».All others:GO to «H14»._________________________________________
H13 CHECK SECONDARY AIR INJECTION (AIR) OPERATION
NOTE:If vehicle is equipped with Pulsed-Secondary Air Injection (PAIR) or no AIR, ignore this step and GO to «H14».
With dual HO2S, DTC 172 refers to right or rear (4.9L SFI Rear) HO2S; DTC 136 and 176 refer to left or front (4.9L SFI Front) HO2S.
HO2S always lean could be caused by:
-- Thermactor air being diverted upstream from the HO2S.
l Disconnect the AIR hose(s) from the AIR pump so that secondary air is bypassed to atmosphere during testing.
l Run Engine Running Self-Test.
l Are DTCs 136, 172 or 176 present?
YesRECONNECT AIR Hose. GO to «H14».
NoFor Continuous Memory DTCs 139, 144, 171, 176, 177:GO to «H90».For DTCs 311, 312 or 313:GO to Pinpoint Test Step «KC1».All others:GO to Section 13A, Test Step «AIR27»._____________________________________________
H90 CHECK CONTINUOUS MONITOR DIAGNOSTIC TEST MODE (DTM)
l Verify engine at operating temperature.
l Start engine and run at 2000 rpm for two minutes.
l With engine rpm at idle enter Engine Running Continuous Monitor (DTM). (Refer to Quick Test Appendix, «Section 5A»).
l Observe VOM or listen for beeper to sound on Super Star II for indication of fault.
l Wiggle, shake or bend a small section of the EEC harness while working your way from the HO2S to the PCM.
l Wiggle, shake or bend a small section of the EEC harness while working your way from the HO2S GND to the PCM.
l Is a fault indicated?
YesISOLATE fault and SERVICE as necessary. REMOVE breakout box. CLEAR Continuous Memory (REFER to Quick Test Appendix, «Section 5A»). RERUN «Quick Test».
NoREMAIN in Engine Running Continuous Monitor DTM.GO to «H91»._____________________________________________
H91 CONTINUOUS MONITOR DTM TEST DRIVE CHECK
l Remain in Engine Running Continuous Monitor DTM.
l Test drive vehicle at 55 mph with minimum road load for five miles.
l Continue to drive on a rough road at 55 mph for five miles.
l If possible, drive vehicle through a pool of water on the road to shower the HO2S and/or connector.
YesISOLATE fault and SERVICE as necessary. REMOVE breakout box. CLEAR Continuous Memory Code. RERUN «Quick Test».
NoEXIT Engine Running Continuous Monitor DTM.GO to «H92».
H92 CHECK HO2S SWITCHING
l Inspect EEC wire harness for proper routing and insulation; burnt, chafed, intermittently shorted or open. Service as necessary.
l Disconnect PCM and inspect for damaged or pushed out pins, corrosion, loose wires, etc. Service as necessary.
l Install breakout box and connect PCM to breakout box.
l Connect analog voltmeter to the suspect HO2S test pin and HO2S GND at the breakout box.
l Test drive vehicle at 55 mph with minimum roadload for five miles.
l Observe voltmeter for HO2S switching from .3 to .9 volt within three seconds.
l Did HO2S voltage switch?
YesUnable to duplicate or identify fault at this time. Clear Continuous Memory DTCs. For further diagnosis, REFER to «Section 7A».
NoREPLACE HO2S. REMOVE breakout box. RECONNECT PCM. RERUN «Quick Test».______________________________________________