PetroStreet

How are the critical instrumented systems maintained, and are the linked to the shutdown systems to maintain or having different category with separately assigned tasks?

I am not sure if I have got your query right.
Just to start with, what are he critical instrumented systems...
ESD
SIS
F&G
HIPPS - High Integrity Pressure Protection Systems
BMS
Critical alarms in DCS
Now are they maintained together with shutdown systems?
Functionally, they are connected but administratively oftern controlled under separate but coordinated frameworks.
Help me understand more what you are looking forward to.

Shutdown systems are often part of SIS architecture but still maintained under a specific shutdown program.
Maintenance too as we have observed with our maintenance teams is also not random.
Every SIF has:
. SIL 1/2/3 rating
. Proof testing interval
. Probability of failure on demand
DUring LOPA and SIL this is all verified.

There are some best practices which can be followed here.
Ideally, the best performing sites would be having:
Dedicated Functional Safety Engineer
SIS Master Register
SIL performance dashboard
KPI tracking (spurious trip rate, overdue proof tests)
Bad actor instrument program
Override time monitoring
Quarterly functional safety audit

Under IEC 61511:
Every Safety Instrumented Function (SIF) must be proof tested at a defined interval to ensure it meets its required SIL.
Now whether they are part of Shutdown Systems to have the checks performed or can be done separately is another thing.