Let ti denote the time of failure of the ith component; let (t) denote the time to

Let ti denote the time of failure of the ith component; let τφ(t) denote the time to failure of the system φ as a function of the vector t = (t1,..., tn). Show that max 1 js min i∈Aj ti = τφ(t) = min 1 jk max i∈Cj ti where C1,...,Ck are the minimal cut sets, and A1,..., As the minimal path sets.