Operating exposure reference

State, load, excursion, and rate methods.

Compact definitions for reconstructing operating exposure from categorical event logs and numeric interval data.

State duration

Duration(state at row i) = timestamp(i + 1) − timestamp(i)
Observed state share = state duration / (last timestamp − first timestamp)

ReliabilityBench treats a row as a change effective at its timestamp. The last row is an open state with no duration. An entry into the exact normalized label RUNNING is counted as one start observation; an exit from RUNNING is counted separately.

Time at load

Hours in band = number of equally spaced readings in band × interval minutes / 60
Mean load = sum(percent-of-rated readings) / number of readings

The load analyzer separates exactly 0% as idle, uses ten positive bands through 100%, and retains values above 100% in a review band. It does not interpolate irregular timestamps or convert between ratings.

Threshold excursion duration

Zone(i) = below if xᵢ < L; above if xᵢ > U; otherwise inside
Zone duration(i) = timestamp(i + 1) − timestamp(i)

Consecutive intervals in the same outside zone form one event. Values exactly equal to a limit are inside. This left-hold convention assumes the current sample represents the interval that follows; the final sample is not assigned time.

Rate of change

Rate(i) = [xᵢ − xᵢ₋₁] / elapsed hours × selected time-base hours

A rise event requires rate greater than the positive rise limit. A fall event requires rate less than the negative fall magnitude. The time base changes reporting units only; it does not smooth or resample the series.

Validation boundaries

Decision boundary

These methods summarize declared source data. They do not establish the correct operating envelope, infer failure causality, calculate degradation or remaining life, quantify sensor uncertainty, replace historian quality flags, or make a safety/compliance decision.