Solution Reliability Evaluation Of Engineering Systems By Roy Billinton And Here
A Hypothetical Excerpt (In the Style of Billinton & Allan)
Title: On the Verification of Solution Reliability in Complex Standby Systems
In the early 1980s, the engineering world relied heavily on "deterministic" rules—basically, safe guesses like "always have one extra generator just in case." Billinton and Allan felt this was too imprecise for modern society. They decided to write a definitive guide to probabilistic reliability, treating power failure not as a fluke, but as a measurable mathematical certainty.
Composite Metrics
4. The Loss-of-Load Probability (LOLP) Index
Perhaps Billinton & Allan’s most famous contribution to electric power (extendable to any capacity-limited system) is the Loss-of-Load Probability (LOLP) .
Frequency and Duration (F&D) Techniques: This method goes beyond basic probability to provide physical indices such as the expected frequency of failure and the average duration of outages. A Hypothetical Excerpt (In the Style of Billinton
Their solution evaluation typically involves a three-step process:
Monte Carlo Convergence Analysis: Static analytical solutions often mask temporal dependencies. Using sequential Monte Carlo simulation (10,000+ years of synthetic operation), generate the system’s time-to-failure distribution. A reliable solution requires the coefficient of variation (COV) of the failure probability to be ( < 0.05 ). If the analytical result lies outside the 95% confidence band of the simulation, the input data (e.g., constant ( \lambda )) is the source of unreliability, not the mathematics. If repair is ignored: The solution overestimates failure
- If repair is ignored: The solution overestimates failure probability by up to 40% for repair times ( < 0.2 \times ) MTBF.
- If switch failures are s-independent: The solution is invalid when switching shares environmental stress with the primary component (e.g., thermal cycling). A correction factor ( C_env ) must be bootstrapped from field data.
Series Systems: A non-redundant arrangement where every component must function for the system to succeed (