The Resilience Model Supporting IIoT System Trustworthiness Y = U ( D y , X ) ( 3 ) Thus by substitution of the ( 2 ) in ( 3 ) we gain : Y = U ( D y , X ) = U ( F ( D x , D SIoT ), X ) ( 4 ) Requirements
Let ’ s now define the requirements to the system behavior from the IT perspective that allow this behavior to remain resilient . That means keeping the Process Output relevant to its IT representation event under adverse conditions . That also means facilitating security and privacy and keeping the appropriate physical process safe and reliable even under the impact of the human factor .
We define the requirements Z = { z i | i ∈ 1 … l } as conditions set for the accountable data in one of the following forms : threshold , equality , optimization . The form of the system requirements is
{⟨ y i ≥ a i | y i = b i | y i → min ⟩}
Conditions that are more complex do not change the reasoning .
Among the system requirements , we highlight the essential requirements that comprise a subset of all requirements and generally determine the conditions that must be kept invariant in any system state .
∃r ≤ l : Z ∗ = { z i }| i ∈ 1 … r } – essential output requirements ;
To consider the system ’ s dynamic behavior , we introduce the time t represented by one of the environment variables .
Definition 1 . System requirements . The IIoT system meets the requirements for any system state and all conditions determining these requirements are satisfied . The appropriate predicate P depending on the system output is true if the system meets all requirements .
P ( Y ( t ), Z ) = TRUE ↔ ∀t ∀i ( y i , z i ) = TRUE ( 5 )
Let ’ s define the Resilience aspect on the basis of the proposed model .
RESILIENCE DEFINITION IN TERMS OF THE PROPOSED MODEL
The Formal Definition of the Resilience Aspect
The basic idea behind the resilience aspect is that the system meets the established requirements in any state . In other words , we assume that the predicate P remains true even under adverse conditions .
Definition 2 . Resilience . The system is considered resilient if in any system state the predicate P is true .
Let ’ s make a substitution in ( 5 ) using ( 4 ) to elaborate on the connection of the Process Output and Process Input in the context of Resilience .
P ( Y ( t ), Z ) = P ( U ( F ( D x , D SIoT , t ), X ), Z )
P ( Y ( t ), Z ) = P ( U ( F < ST , C , R > ( D x , D SIoT )( t ), X ), Z ) ( 6 )
Formal Consideration of Resilience Goals
Using this detailed expression , we now consider the Resilience goals defined in Draft NIST Special Publication 800-160 VOLUME 2 : anticipate , withstand , recover and adapt .
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