I'm in agreement with DekDee regarding renumbering PQRs. There should be no need to renumber existing PQRs since they are supporting documentation for the WPS. Once the PQR is established, it isn't changed unless there is a code change that affects the information recorded by the PQR. One such change would be the filler metal specification. AWS is changing the filler metal specification for carbon and low alloy steels. AWS A5.34 will include the current A5.18 and A5.28. Metal cored electrode will be regrouped with FCAW electrode as A5.36. That specification will incorporate the electrodes currently listed in A5.20 and A5.29. If you currently have a PQR listing the GMAW electrode as A5.18, it will be changed to A5.34 on the PQR. You would retain the original information that was recorded when the PQR was written. However, the new information would be recorded as a revision and perhaps a note listing the reason for the revision.
You can reidentify the WPSs as a revision to make it easier to find the applicable WPS. The ID system can be a rational alpha-numeric system. Since you mentioned Inspection Trends you will remember that the system in the article listed the welding process, the base metals, and the filler metal. Most welding standards group the base metals as P numbers, Group numbers, or M numbers. The filler metals are grouped by F numbers.
The system makes it easier to identify what the WPS applies to. Some companies assign a number to each welding process, i.e., 1 for SMAW, 2 for SAW, etc. I don't care for that system because the welder or the individual tasked with looking up a WPS needed to know the secret code. I like the system where the welding process identification is more intuitive, SMA for SMAW, GMA(P) for gas metal arc welding using pulsed spray, etc. Whether you use a P-number, Group number, S-number, etc. is dependent on the specific welding standard being used.
A suffix letter can be added to differentiate the WPS from one that is similar. For instance, if the WPS is qualified for notch toughness, it could be assigned an identification such as: GMA(P)-1/1/6-N. If working to ASME a WPS qualified for notch toughness needs to be more specific. The WPS is limited to the P-number and group number, so GMA(P)-1-1/1-1/6-N might be sufficient.
Some people get up tight when the identification becomes too long, but anyone that has had to search through 100 plus WPSs to find one suitable for the job knows it ain't no picnic to thumb through WPS-001, WPS-002, ....... until the correct one is located.
In short, I like any rational system that identifies the key information needed to determine if the WPS is appropriate for the work.
You can adopt a similar system for PQRs when qualifying new WPSs. Just remember each WPS and PQR has to have a unique identifier.
Example: PQR: GTA(P)-1/8/6-250 stands for PQR, Gas Tungsten Arc Welding - pulsing, M1 base metal welded to a M8 base metal, using an F6 filler metal, and the test assembly was 1/4 inch thick.
The rational identifier assigned to the WPS and the PQR indicates most of the pertinent information, the essential variables that differentiates it from another WPS or PQR.
Good luck
Best regards - Al