I just wanted to ask if there exists anything like a Hard-time RTOS or Soft-Time RTOS itself or is it the designer who defines a system as Hard-time or Real-time irrespective of the RTOS used?
Are Real time systems Hard/Soft or the RTOS itself?
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Most people implicitly have an informal mental model that considers information or an event as being “real-time”
--if, or to the extent that, it is manifest to them with a delay (latency) that can be related to its perceived currency
--i.e., in a time frame that the information or event has satisfactory usefulness to them.
Note that the magnitude of the delay is irrelevant, it may be from microseconds to megaseconds. Well known examples in the real world include real-time computing systems, automated financial trading, and adverse weather alerts.
Any particular real-time system (i.e., according to the above informal mental model, it has satisfactory timeliness), which includes an OS, depends on that OS to be real-time enough--i.e., have latencies short enough that result in it providing satisfactory usefulness to the rest of the system. Some systems may be real-time enough even though the OS is Microsoft Windows (numerous such systems are deployed); other systems cannot be real-time enough unless their OS is designed and implemented to have very low latencies.
The informal mental model refers to timeliness but lacks the second essential property of something being "real-time:" predictability of timeliness.
Usually an OS which is intended for real-time systems is designed and implemented to have sufficiently low latencies (needed for timeliness) AND sufficiently high predictability of latencies (and hence timeliness). Again, note that the magnitudes of the latencies and the degrees of predictability are application-specific. An OS or a system can have latencies in (say) seconds or minutes, and predictability of timeliness which is stochastic (e.g., long low value tails after the mean value, which is common in many real-time systems and RTOSs).
Predictability is an extremely deep topic, especially in real-time systems.
It is discussed elsewhere.
"Hard" or "Soft" is a characteristic of the system requirement. It is unrelated to the RTOS used.
See this related question for more information.