# 8.2 PFGE Method

*T*_{il} and *T*_{ip} are random variables respectively representing the time‐to‐local‐failure and the time‐to‐PFGE of a system component *i*. *f*_{il}(*t*) and *f*_{ip}(*t*) represent the probability density function (*pdf*) of *T*_{il} and *T*_{ip}, respectively. *q*_{il}(*t*) and *q*_{ip}(*t*) are unconditional local and propagated failure probabilities of component *i* at time *t*, respectively. Thus,

According to the simple and efficient algorithm (SEA) in Section 3.3.2 [ 2 ,4], the system unreliability can be evaluated based on the total probability law as:

with *P*_{u}(*t*) being defined and computed as

*Q*(*t*) in 8.1 is defined as a conditional system failure probability given that no PFGEs take place during the considered mission time. The evaluation of *Q*(*t*) requires...