Weibull Repose Failure Probability
Evaluate conditional Weibull renewal probability given no event through elapsed repose, using supplied fitted parameters and stable hazard increments; model probabilities are not validated volcano-specific eruption risk.
Description
Repose is the time between eruption onsets.
Repose is the time between eruption onsets. A Weibull renewal model describes how a fitted event-time distribution changes after an event-free interval.1
Evaluate conditional Weibull renewal probability given no event through elapsed repose, using supplied fitted parameters and stable hazard increments; model probabilities are not validated volcano-specific eruption risk.
When to use Weibull Repose Failure Probability
Use this tool to evaluate conditional Weibull renewal probability given no event through elapsed repose, using supplied fitted parameters and stable hazard increments; model probabilities are not validated volcano-specific eruption risk.
Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
How to use Weibull Repose Failure Probability and understand its results
- Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
- Enter weibullScaleYears, weibullShape, elapsedReposeYears, futureWindowYears using the field table and calculation rules, then run the tool.
- Read conditionalModelEventProbability, cumulativeModelEventProbabilityByWindowEnd. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| weibullScaleYears | Weibull scale years | number | Required |
| weibullShape | Weibull shape | number | Required |
| elapsedReposeYears | Elapsed repose years | number | Required |
| futureWindowYears | Future window years | number | Required |
Use positive scale and shape and nonnegative elapsed and future years. Compute cumulative hazards at both endpoints; stable log1p/expm1 arithmetic preserves small hazard differences. A zero future window returns zero conditional probability.2
P(event in window | survival to t) = 1 − exp(−[((t+h)/scale)^shape − (t/scale)^shape]) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| conditionalModelEventProbability | Conditional model event probability | number |
| cumulativeModelEventProbabilityByWindowEnd | Cumulative model event probability by window end | number |
{
"input": {
"weibullScaleYears": 10,
"weibullShape": 2,
"elapsedReposeYears": 10,
"futureWindowYears": 10
},
"output": {
"conditionalModelEventProbability": 0.950212931632136,
"cumulativeModelEventProbabilityByWindowEnd": 0.9816843611112658
}
}Limitations and assumptions
Parameters must already be fitted. Renewal assumptions, catalog completeness and volcano-specific validation are outside this calculation.
Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Repose Interval Recurrence Mean: Summarize complete historical repose intervals separately from right-censored time since last onset; not a survival-corrected mean recurrence estimator or deterministic next-event forecast. For a complementary task, use Time Predictable Next Eruption Estimator: Fit the time-predictable previous-eruption-volume/subsequent-repose hypothesis and interpolate a last-volume scenario; this historical calibration is not a reliable next-eruption date or an uncertainty interval.
Further background: Weibull distribution and cumulative hazard.
References
Similar or alternative tools
- Repose Interval Recurrence Mean
Summarize complete historical repose intervals separately from right-censored time since last onset; not a survival-corrected mean recurrence estimator or deterministic next-event forecast.
- Time Predictable Next Eruption Estimator
Fit the time-predictable previous-eruption-volume/subsequent-repose hypothesis and interpolate a last-volume scenario; this historical calibration is not a reliable next-eruption date or an uncertainty interval.