For the first case, the control valve would be the final control element in the SIF and this SIF would need to have a  rating equal or greater than 1.

For the second case, Riyaz cites part 1 clause 11.2.10 which states that a device used to perform part of a safety instrumented function shall not be used for basic process control purposes, where a failure of that device results in a failure of the basic process control function which causes a demand on the safety instrumented function, unless an analysis has been carried out to confirm that overall risk is acceptable. He notes how this may be interpreted:

• YES: If all possible failures of the control valve do not place a demand on any SIF than control valve may be used with no further analysis. In this case, Control Valve is "Final Element" of Safety Instrumented Function (SIF) Loop, needs to have SIL rating equal to or above 1.
• NO: If failure of the control valve will place a demand on a SIF than it may not be used as the only final element in that SIF.
• If failure of the control valve will not place a demand on SIF, for which it is intended but may place demand on any other associated SIF than the control valve may be used in a SIF only after detailed analysis. An additional step to further analysis will be necessary in these cases to ensure that the dangerous failure rate of the shared equipment is sufficiently low.

The control valve in this case would again be the final element of a SIF requiring a SIL rating greater than 1.

In the third example of providing additional hardware fault tolerance for higher SIL applications, mean time to fail (MTTF) of the control valve can be used in the probability of failure on demand (PFD_avg). He shares the failure fraction components and equations for arriving at the PFD_avg of the SIF. For this 3^rd case, Riyaz shares [links added]:

...mechanical equipment like valve bodies and actuators do not have any diagnostics capabilities. According to part 2, table 2, with a hardware fault tolerance (HFT) of zero, they can only be used in SIL 1 applications. A digital valve controller mounted on a "Final Control Element" improves the diagnostic coverage factor, which in turn improves the SFF number, allowing the possible use of higher SIL rated applications (Per IEC 61508 part 2, table 3) by use of the Partial Stroke Test.

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