[__s]

Without knowing the scale of company you're at it's hard to give advice

At Microsoft I headed Incident Count Reduction on my team where opex could be top priority & rotating on call would have a common thread between shifts through me (ie, I would know which issues were related or not, what fixes were in the pipe, etc)

I'm guessing the above isn't an option for you, but you can try drive an understanding that while someone is on call there is no expectation for them to work on anything else. That means subtracting on call head count during project planning

[frugal10]

The team size is 7 people. The organization is medium in size with around 3k employees. The business unit that i work in is relatively in 0-1 stage. So there is some amount of chaos and adhoc requirements coming every now and then