A good drive will tell you if you solved the problem or not.. CPS is a tricky thing to test regardless of how the manual tells you so. In BMW, it is very very very common to go bad. in older MB of same era or older... not common at all. The new MB has CPS problem at higher mileage... typical symptom will be engine dying when engine is hot... pretty consistent to temperature. In winter... not so much.

Other thing with CPS is that you might notice the engine is running hotter with faulty but functioning CPS. After change, the engine runs cooler. This is observed on my friend's MB.