Is Reliability Component a vertex? The term component has a distinct definition in graph theory from vertex while the terms components and vertices can be mostly the same in Realiability Engineering, my intuition. So how is the term component Operations Research (OR) such as Reliability Engineering usually defined?
Is the reliability component a vertex as defined in graph theory?

Consider




where the source is the book System Signatures and their Applications in Engineering Reliability. Springer preview is here.
I recited on the thinking in chat here where I came to conclusion that a component (reliability term) is a vertex (graph theoretical term).
Puzzles

I. set of all the systems's components equal {1,2,3,4,5}? Or is this wrong?
II. algebraic union of all minimal path sets is?
III. what does "minimal path sets consist of the collection $\{\{1,4\},\{1,3,5\},\{2,5\},\{2,3,4\}\}$ mean?

Answers

III. minimal path sets = {{1,4},{1,3,5},{2,5},{2,3,4}}
II. Algebraic union of all minimal path sets is U_i S_i= {1,4}\cup {1,3,5}\cup {2,5} \cup {2,3,4}={1,2,3,4,5}
I. set of system's components equal to {1,2,3,4,5}


Example 1.
Notice that the bridge system in Fig.2.2. does have the component $\{1,2,3,4,5\}$ by the property (ii) even though not minimal.
