Used for systems with low component failure rates (e.g., transmission lines fail 0.1 times/year).
Following Billinton’s methodology, a "solution" is not complete unless it produces specific, actionable indices. For a practical engineering system, these include:
| Index Category | Specific Index | Definition (Billinton’s phrasing) | | :--- | :--- | :--- | | Probability | LOLP | Probability that the load will exceed available capacity at a given time. | | Frequency | LOLE | Expected number of days (or hours) per year that a deficiency exists. | | Duration | LOLD | Average duration of each deficiency event. | | Energy | EENS | Expected Energy Not Supplied (in MWh). Used for economic costing of failures. | | Customer | SAIFI | System Average Interruption Frequency Index (customer-centric). | | Customer | CAIDI | Customer Average Interruption Duration Index (restoration speed). | Used for systems with low component failure rates (e
Billinton’s Critical Contribution: He proved that EENS (Expected Energy Not Supplied) is the single most valuable index for cost-benefit analysis. If you cannot monetize the reliability solution, you cannot justify the investment.
Before evaluating reliability, Billinton insists on a precise definition of the "solution." In his framework, an engineering system is reliable if it satisfies three conditions: The "solution" to a reliability problem, therefore, is
The "solution" to a reliability problem, therefore, is not a single number but a set of probabilistic indices that quantify the frequency, duration, and magnitude of failures. Billinton famously argued that a deterministic "margin" (e.g., 15% spare capacity) is a poor solution because it ignores the stochastic nature of component failure and load variation.
No solution is perfect. Billinton’s framework, as published in the 1980s-90s, assumes stationarity (failure rates are constant) and independence (component failures don't cascade initially). Modern engineering systems (smart grids, cyber-physical systems) violate these assumptions. However, even these extensions use Billinton’s core logic:
Modern researchers now extend the "Billinton solution" to include:
However, even these extensions use Billinton’s core logic: Define the state space, calculate the probability of failure, multiply by consequence.