System Reliability Modeling
Industrial facilities comprise interconnected subsystems. An RBD transforms physical plant diagrams into probabilistic success logic, revealing single points of failure (series links) and evaluating redundancy configurations (parallel and k-out-of-n).
Mathematical Formulations
Series System: Rsys = ∏ R_i
Parallel Redundancy: Rsys = 1 - ∏ (1 - R_i)
k-out-of-n Identical: Rsys = ∑i=kn (n! / (i!(n-i)!)) · R^i · (1 - R)^(n - i)
Birnbaum Importance: I_B(i) = ∂Rsys / ∂R_i = Rsys(R_i=1) - Rsys(R_i=0)
Worked Example
A steam boiler system requires at least 2 out of 3 feedwater pumps operating (2-of-3 redundancy). Pumps A and B have 92% reliability, while Pump C has 88% reliability. The overall system reliability computes to 97.2%, achieving higher availability than any individual pump.