The most important tools for appraising QIPs are CMMI and SPICE / ISO 15504 / ISO 330xx. There are different variants of these models, depending on the industry you are looking at, and several differents versions were created over time.
I agree with Ralf, and want to add, it depends on what the particular thing is you are improving. Usually a tool is used from beginning to end of the project.
Any QIP is introduced for a specific objective. The objective is clearly defined (and sometimes redefined) during the Plan stage of PDCA.
After implementing the project, you come to the CHECK and the ACT stages of PDCA. You need to compare your CHECK inferences with the PLANNED objectives and ACT on any deviations.
This comparison between the achievement and the plans is what will tell you the success level of the QIP.
Again, verifying the effectiveness of the QIP after a pre-planned period is also a must to appraise the QIP.
Thus PDCA and verification of effectiveness are the two -you may call tools to appraise the QIP.