System Settings
System Configuration
Number of Components
4
MTTR (Mean Time To Repair)
10 h
Component Reliability
—
R_system
—
MTTF_system (h)
—
System Availability A
—
Most Critical Component (max Birnbaum)
—
Improvement Margin ΔR_s
RBD Block Diagram
R_system(t) Time-Dependent Reliability
Birnbaum Importance
Formulas
Series: $R_s = \prod_i R_i$
Parallel: $R_s = 1 - \prod_i(1-R_i)$
k-out-of-n: $R_s = \sum_{i=k}^{n}\binom{n}{i}R^i(1-R)^{n-i}$
Time-dependent: $R_i(t)=\exp(-\lambda_i t)$
Availability: $A = \dfrac{\text{MTBF}}{\text{MTBF}+\text{MTTR}}$
Birnbaum importance: $I_B^{(i)} = \dfrac{\partial R_s}{\partial R_i}$
CAE Integration: Redundancy design evaluation for mechanical drivetrain systems / Redundancy optimization for aerospace control systems / Preliminary SIL (Safety Integrity Level) calculations for process industries / Usable as input for the Occurrence (O) score in FMEA.