As we know, BMW cars are developed and also manufactured in Germany. Accordingly, we can hope that precisely Germany is the country where these cars get the best service. Who else, except the dealer, would be able to ensure the most excellent service. German specialists have no language or mileage barrier (not in direct or indirect means). And still – one of many cases which confirms: the knowledge and understanding of the BMW dealer network are at a shallow level.
The owner of the N43 series BMW approached me. The idle of the car is uneven. The dealer has replaced the injector of the 4th cylinder. In addition, did it TWO times! Without result. The dealer has replaced the timing chain. Without result. I believe it is clear to everyone – these repairs were expensive.
Let’s check the error message history lists.

Yes, the 4th cylinder has been turned off (due to misfires). We see that the fuel mixture in the 1st bank has been too rich (we can assume that some of the injectors of the 1st bank have been leaking). But, we also see the error message 30EA (this error message has been recorded nonstop!).

30EA means – the NOx catalytic converter is contaminated, the desulfation section should be activated and the catalytic converter should be cleaned (driving with a speed of 110+ km/h). The dealer was not able to solve this problem. Or rather, the dealer had no idea how to do it. The customer was fed up with this fight and installed the NOx emulator. The emulator solved the NOx system’s problems, but the vibration was still present.

Here we see that the DME has identified problems with the EGR valve. Unfortunately, the dealer was not able to notice nor solve the problem.
I checked all error message lists and didn’t find any signs that could indicate any problems with the timing chain (for example, non-compliance of camshaft reference). My experience and all data say that the chain replacement was utterly unjustified!
Good news – the dealer has managed to install positions of the camshafts more or less correctly.
The error message list confirms the old problems with the EGR valve. The 4th cylinder is still turned off. After re-adaptation of the engine (the dealer has not performed this procedure – this already is a violation of the service procedure), the error message regarding Lambda probes appears (DME is unable to trim Lambda probes, etc.).
Here is the data of the injectors.
Stratified charge, idle:

With yellow, I marked the data of the injector of the 1st cylinder. Reduced efficiency – either insufficient atomization or reduced “speed” of the injector/ injected fuel amount for short openings.

Stratified charge, partial load:

Significant flowrate difference between cylinders No.1 and No.4. The injector of the 1st cylinder – with strongly reduced (for 25 .. 30%) flowrate.

Injector opening times, idle:

Opening time of the 1st injector – increased. Also, in the Homogenous mode, the injector is “less efficient”.

Video screens of the cold start.

One of the injectors of the 1st banks is leaking.

This menu clearly shows – the 1st injector of the 1st bank is leaking. Accordingly, DME tries to “regulate” the average fuel mixture of the 1st bank, the fuel mixture in the 4th cylinder becomes lean, and the misfires start in it. Typical situation!

Also, the freeze-frame of the error message regarding turning off the cylinder indicates:

misfires started:
a. for cold/partially warmed-up engine;
b. in idle (when the impact of the leaking injector is at max);
c. the Integrator of the 1st bank is -25%, which means – one of the injectors of this bank has been leaking.
One more confirmation of the problem with the leaking of the injector of the 1st cylinder.

Here is the confirmation of the problems with the EGR valve:

As we see, the adaptations of the wide opening position (4.736 V) are very close to the critical level (4.800 V). Obviously, sometimes this critical level is reached.

Unfortunately, this typical situation was way too complicated for the BMW dealer. I say “way too” because even after the first replacement of the injector, the “specialists” of the dealer had no idea what could be the actual culprit. The only thing they could imagine – replace the same injector once again! BMW dealer does not trust the spare parts sold by themselves? Interesting…