Ford F-150 Misfires in Ford Gas engines
There are 4 major causes of misfires
1. Spark plug and boot issues.
2. Coil related issues.
3. Fuel related issues.
4. Any cylinder mechanical issues.
Any combination of the above.

How is misfire detected?
A. System actually measures Crank rotation time on every cylinder in the order, from the Crank sensor signal.
B. When a cylinder is too slow in time for any reason it is a Logical misfire to the operating program.
C. These misfires trigger a code in the P0301 to P0310 group of codes.

A second set of codes in the P0351 to P0360 can be set when an electrical failure is detected in the Coil primary circuit.
The Computer monitors the current waveform for coil action and compares it to a known profile. This is not a time related function but strictly electrical.
This type failure can be the coil, the connector, the harness or the computer coil driver.

How to test the coil driver
Use an Ohm meter that will read 10,000 ohms resistance to look back at the coil driver in the computer. It needs to read about that value, not greatly higher or greatly lower. This was designed into the computer so it could be measured from outside for reasonable diagnostics of the issue.
If the resistance is found to be very high to open or very low to shorted, the computer must be replaced with attendant programming requirements.

Special misfires that do not set a code
In a normal driving mode of Overdrive and light throttle application, the computer opens the Exhaust Gas device to allow some exhaust gas to enter the intake tract. This leans out fuel injection, advances ignition timing and leans out the Air/Fuel ratio for combustion.
Under these conditions the coil voltage required goes up a large amount to fire that lean mixture.
If a coil is unable to fire the charge reliably a misfire results. It would feel like an intermittent stumble in drivability. This stumble usually goes away with down shift or exits from Over drive.

What is the cause?
A coil that has 'shorted turns' in it's wire winding limits the magnetic field that produces the high voltage required to a lower value causing the misfire.

Why does it not set a code?
This type of coil fault is not a hard fault meaning neither an open or a dead short that would have been detected by the above methods.
When the trouble goes away, the computer cancels the misfire record in the normal history location because it's no longer present until the next time.

How to detect which cylinder has the faulty coil
Using a good Scanner to look into live memory locations, mode 6, test 53 holds any misfire counts for each cylinder.
Since this location has no ability to set any codes, you must look to see which cylinder has the high counts out of limits.

Other misfire causes
1. Faulty spark plug and or Boot.
2. Fuel injector plugged or not operating.
3. Coolant from a leak getting into the plug Well.
4. Blown head gasket allowing coolant into cylinder.
5. Any mechanical cylinder fault. Head gasket, valves, piston and rings etc. that cause loss of power.
6. Intermittent electrical connectors on coils, injectors, harness or Crank sensor.

Do not ignore a flashing CEL lamp because the system has decided a misfire can pass raw fuel through to the cat converters and light off there causing very high temperatures that melt the cat substrates.
This can cause exhaust blockage and results in expense far above the cost of the original misfire cause.
Very often the rear Ox sensor goes with it.

Bottom line is to diagnose the misfire issue according to proper operation and knowledge and not guess or replace parts hoping you get the cause.