Imaging following situation:
The SDLC begins in a software house at the point of "Low-level Design" and ends with "Unit & Package Tests".
Other parts of the SDLC (Business Req Analysis, High-level Design and System Integration, System Test, UAT) are done direct by concern internal customer of this software house.
Is it sensible & achievable - at this situation (the above mentioned "not active processes" are described, but recently not lived) - the software house can get CMMI Level 3 certification ?
Oh, you want sensible AND achievable? Picky picky picky..... :)
On the face of it (and not knowing much about your company) I can see where you might think you have a problem. After all, the CMMI requires you to be performing ALL of the Process Areas in a Maturity Level (and all of the levels below it) in order to be appraised , and the only exception allowable is to leave Supplier Agreement Management being out of scope (this is by no means a “given” by the way, but it does happen).
So I would start with a question. “Do you really have a problem?”
Let’s take Requirements Development (a ML 3 PA) as an example. You’ve implied that your customer supplies you with requirements in a way that allows you do jump right to low-level design. Is that always true? Do they supply you with true requirements, or simply with their needs? Do you spend any time “fleshing” out the requirements so that it’s clear what they mean? Do you ever “derive” requirements from your customer’s needs (derived requirements could be based on technical, regulatory, legal, process, organizational, or any other source that your customer had not considered)? Do you break requirements into “component requirements” or “sub requirements so that they can be allocated to designs?
If you do any of those things you are performing parts of requirements development. You may not ALWAYS be performing ALL of Requirements Development practices, but you are probably are performing the right amount for your business environment.
You’ve also indicated that there are other process areas outside of your scope. It’s possible that some of these things could treated as “Supplier” activities if they are done on behalf of your company, or some of them could be jointly appraised with your business partner for level 3, or for some of them you may even be performing more of the process than you think.
It may be "sensible" to include your customers as part of the appraisal of they can come to understand the value of what you're trying to do. In the end, they will benefit as much as you will from the effort.
Either way, I would recommend you connect with a CMMI Lead Appraiser as soon as possible to visit your site, speak with your stakeholders, and give you some specific recommendations for moving forward.
Best of luck to you!