Your question is confusing. Mandatory Appendix E in ASME Section IX refers to endorsed Standard Welding Procedure Specifications (SWPS) issued by AWS.

Dear metengr
Yes you right but if you consider the content of the table you can see that it refer to for example (M-1/P-1/S-1)

Ok, I now understand your question. The M-No material designation is unique to AWS because they are the organization that develops the Standard Welding Specification Procedure and they develop their own Welding Standards (I have AWS D14.6 and materials are classified using M in this Standard). They follow the same nomenclature as ASME Section IX, however for those materials not identified by either a P-No or S-No, AWS assigns an M-No to broaden the range of materials.

Thanks for your good information. it's clear for me now.

The M numbers are listed in AWS B2.1 Specification for Welding Procedure and Performance Qualification. The M number for carbon steel and low alloy steels seems to be based on carbon equivalency.

For the most part, the M numbers correspond to the P numbers used by ASME. However, the listing of M numbers includes both P and S numbered materials found in ASME and includes materials not included in the ASME B&PV codes.

Best regards - Al