Industry: Utilities
Product: ModelRisk
Application: Grid reliability analysis

The Reliability Target Looks Met at 78 Minutes — Until the Distribution Puts P(Breach) at 25%

A 1.35-million-customer distribution utility reports its reliability to the regulator as two numbers: SAIDI (System Average Interruption Duration Index, in interruption-minutes per customer per year) and SAIFI (System Average Interruption Frequency Index, interruptions per customer per year). The planning team's deterministic workbook multiplies the expected interruption rate (1.00 per customer) by the expected restoration time (78 minutes) and reports a tidy 78-minute SAIDI — comfortably inside the regulator's 110-minute target. The board signs it off.

The problem is that SAIDI is not a number; it is the outcome of a year, and years differ. A bad-weather year pushes storm outages, vegetation contacts and stretched restoration times up together, because they all respond to the same weather. Run the year 200,000 times in ModelRisk with that shared driver in place and the mean SAIDI is 91 minutes, the median is 67, and the 90th percentile is 178 minutes — well past the target. One simulated year in four breaches the 110-minute target. The deterministic 78-minute figure is not just optimistic; it is a number that essentially never occurs.

Why a point estimate fails here

The deterministic calculation treats every cause as if it fired at its long-run average and treats restoration time as a fixed constant. Two things break that:

• Restoration time is right-skewed, not fixed. Most interruptions are cleared quickly, but a minority — cable faults that are slow to locate, storm damage across many spans — run long. Average-restoration-time × average-frequency systematically understates a quantity built from a heavy-tailed product.
• The causes are correlated through weather. A severe storm season does not raise one cause by its average; it raises storm interruptions, vegetation contacts and restoration times at the same time. Summing independent causes would wash that correlation out by the central-limit effect and produce a deceptively narrow bell. The tail only appears when the shared weather-severity factor is modelled explicitly.

In ModelRisk the annual weather-severity factor is a single Gamma draw per simulated year (mean 1.0, right-skewed) that multiplies every weather-sensitive cause and lengthens restoration. Frequencies are modelled as over-dispersed (Gamma-Poisson) counts rather than thin Poisson noise, so even a fixed-weather year still clusters.

The annual SAIDI distribution

The headline chart is the full distribution of annual SAIDI across 200,000 simulated years. The mean is 91 minutes per customer, the median 67, the P90 178 and the P99 419 — a long right tail driven by severe-weather years. Against the regulator's 110-minute target, the probability of breach is 25%: a one-in-four chance the utility reports a year that triggers regulatory scrutiny and penalty exposure. The deterministic 78-minute estimate sits below even the median, which is exactly why it never triggered a warning.

SAIFI tells the same story in frequency terms: mean 1.00 interruptions per customer, P90 1.54, and a 34.6% chance of breaching the 1.05 SAIFI target.

What drives the tail

The tornado ranks the inputs by their effect on P90 SAIDI (the 178-minute figure). The annual weather-severity factor dominates, swinging P90 by about ±34 minutes on its own — confirming that the correlated weather driver, not any single equipment parameter, owns the tail. Vegetation-contact frequency is second (±19 minutes) and restoration-time dispersion third (±16 minutes). The point estimate's blind spot — treating weather as a constant — is the single largest source of the reliability risk it failed to show.

Where the minutes actually come from

Decomposing the 91-minute mean SAIDI by cause shows where investment earns its return. Major-storm / weather contributes 35.5 minutes (39%), vegetation contact 23.7 minutes (26%) and equipment age / cable faults 22.3 minutes (24%); animal/contamination and other causes together add under 10 minutes. Three causes account for roughly 89% of the mean — and two of them (storm and vegetation) are the weather-sensitive ones that drive the tail, so cutting them improves both the average and the breach probability.

What the model changed

The team tested three hardening programs against the same simulated weather draws, so the comparison holds the year-to-year luck constant:

• Baseline: mean 91 min, P90 178 min, P(breach) 25%.
• Vegetation program (−45% tree-contact): mean 80 min, P90 156, P(breach) 20%.
• FLISR automation (−30% restoration time): mean 60 min, P90 117, P(breach) 11%.
• Combined hardening program: mean 53 min, P90 103 min, P(breach) 9%.

Only the combined program pulls the P90 (not just the mean) inside the 110-minute target and cuts the breach probability from one-in-four to under one-in-ten. Because the levers attack the weather-sensitive causes, they compress the tail rather than just shifting the body — the exact failure mode the deterministic study could not see. The filing now reports SAIDI as a distribution with a stated 25% breach probability and a clear remediation path, rather than a single 78-minute figure the regulator would never have been able to reconcile against the year-end actuals.

ModelRisk functionality used

• Shared Gamma weather-severity factor drawn once per simulated year, multiplying every weather-sensitive cause and lengthening restoration — the correlation that creates the SAIDI tail.
• Gamma-Poisson (over-dispersed) interruption counts per cause, so frequency clusters realistically instead of behaving as thin Poisson noise.
• LogNormal restoration-time model feeding SAIDI = SAIFI × CAIDI, with restoration stretched in severe-weather years.
• Percentile and exceedance reporting — mean, median, P90, P99, and P(SAIDI > target) — replacing the single deterministic point estimate.
• Tornado sensitivity ranking drivers of P90 SAIDI, isolating the weather factor as the dominant tail driver.
• Scenario comparison on common random numbers, scoring four investment paths on the same weather draws so the program effect is not confounded with simulation luck.

Reliability indices are reported as single numbers, but they are the result of an uncertain year. Modelling that year explicitly in ModelRisk turns "78 minutes, target met" into "91-minute mean, 25% chance of breach, and here is the program that fixes it" — a far more defensible position in front of a regulator.