Multiple arrays used as you have in your formula basically evaluate the formula by aligning the various arrays and using each set independently (i.e. YAEL+T01, YAFD+T02). This is not what you are looking to do.
I'm sure there are other methods to achieve what you're looking to do but the one that sprang to mind was the use of Sumproduct. I'm not sure how long you've been using Excel, but for a long time Sumproduct was the best way to perform a multi criteria Countif. Taking your formula above and converting it we get:
=SUMPRODUCT(--(Master_tbl[Erfassungsdatum]>="01.01.2017"),--(Master_tbl[Erfassungsdatum]<="31.01.2017"),--(ISNUMBER(MATCH(Master_tbl[Auftragsart],{"YAEL","YAFD","YALP","YAPL"},0))),--(ISNUMBER(MATCH(Master_tbl[IH-Leistungsart],{"T01","T02","T03","T04","T35"},0))),--(Master_tbl[P/AP]="AP"))
ISNUMBER(MATCH...essentially converts what would be a multidimensional array (if you were doing the simple comparison of column = {array}) into a single dimension, which can then be combined with the other criteria comparisons.
I wasn't entirely sure what the format of your Erfassungsdatum column is so the comparison for those assumes a string value. If it's a date you'll want to adjust accordingly.
I'm not 100 percent, but i don't think you can use the 2 arrays in one instance like this, i have tried before myself and got odd results. as a work round try and use a helper column to do the 2 countifs independently, and then a count if on those where there is matches, hope that helps – PeterH – 2017-11-07T13:20:43.010
@User91504: thanks for your comment. The problem is that there is no possibility to add a helper column, otherwise you are right. – Dio – 2017-11-07T13:24:29.110
@Dio Can you please show some screenshots? I do know what you are asking for is possible. If you provide me the example you are working with, I can provide you a solution that matches what you have better – Eric F – 2017-11-07T13:38:35.753
@Eric I added some screenshots, but I am not sure if it is clear, becaue the table is too large. – Dio – 2017-11-07T14:00:58.370
@Dio Thanks however it seems you have two answers below anyways which hopefully do help you out :) – Eric F – 2017-11-07T14:01:49.163