Unlike state sampling, sequential simulation steps chronologically through time. Component lifecycles are simulated by sampling their state duration distributions using inverse transform sampling:
In a series system, the failure of any single component results in total system failure. The overall reliability ( Rscap R sub s ) of a system with
[Start Simulation] │ ▼ [Sampling State Transitions via Random Numbers] │ ▼ [System Chronological History Simulation (State Duration Coding)] │ ▼ [Is Convergence Criteria Met?] ──► No ──► [Repeat Sampling] │ ▼ Yes [Extract Reliability Indices (LOLE, EENS, ECOST)] │ ▼ [End Simulation] “Redundancy without analysis is just expensive hope
The expected lifespan of a non-repairable component.
[ Engineering System Reliability Evaluation ] │ ┌──────────────────┴──────────────────┐ ▼ ▼ [ Analytical Methods ] [ Simulation Methods ] ├─ Network Modeling └─ Monte Carlo Simulations │ ├─ Series Configurations ├─ State Sampling │ ├─ Parallel Redundancy └─ Time Sequential │ └─ Complex Standby Modes ├─ Markov Calculations └─ Fault Tree Analysis The Bathtub Curve and Failure Rates Unlike state sampling
Fault Tree Analysis uses logic gates (AND, OR) to map the top-down paths leading to an undesirable system event.
A classic mistake: treating all failures equally. Billinton’s genius was separating from inconvenience . “Redundancy without analysis is just expensive hope
“Redundancy without analysis is just expensive hope.”
), engineers can solve systems of differential equations to determine long-term steady-state probabilities for complex engineering systems. Simulation Solutions: The Monte Carlo Approach
T=−ln(1−U)λcap T equals negative the fraction with numerator l n open paren 1 minus cap U close paren and denominator lambda end-fraction