9.4 System with Random Failure Propagation Time
The methods presented in Sections 9.2 and 9.3 assume that any failure propagation originating from a system component instantaneously takes effect, which is often not true in real‐world cases . In this section, a combinatorial method is presented for addressing random propagation time (PT) in the reliability analysis of single‐phase systems subject to the competing probabilistic failure isolation and failure propagation effects.
9.4.1 Combinatorial Method
The method involves a six‐step procedure described as follows:
- Step 1: Separate effects of PFGEs from the trigger component. According to the PFGE approach (Section 8.2), the system unreliability is evaluated as
UR system t = 1 − P u t + Q t · P u t ,
where Pu(t) = P(no PFGEs from the trigger, e.g. R),
--t (denoted by XSF(t)) given that the trigger undergoes no PFGEs (denoted by Q t = P X SF t | X Rp C t -- evaluated through... X Rp C t