Weibull Reliability Calculator
Conditional two-parameter Weibull reliability exp[−(t/η)^β], independently calibrated nonnegative time and positive scale/shape. No parameter fit or validated prediction. Actual independently established compatible units/model context; conditional arithmetic, not code compliance, engineering design or safe-operation approval.
Description
A two-parameter Weibull survival model depends on a calibrated time scale and shape.
A two-parameter Weibull survival model depends on a calibrated time scale and shape.1
This tool evaluates its conditional reliability without fitting parameters or establishing a validated individual prediction.
When to use Weibull Reliability Calculator
Use this tool to evaluate its conditional reliability without fitting parameters or establishing a validated individual prediction.
How to use Weibull Reliability Calculator and how it works
- Prepare elapsedTime, callerCalibratedWeibullScale, callerCalibratedShape, with the units, conventions and assumptions below.
- Enter the required fields and run Weibull Reliability Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| elapsedTime | Nonnegative elapsed time t in the same time unit as the scale parameter. | number | Required; nonnegative; finite; other constraints below |
| callerCalibratedWeibullScale | Independently calibrated positive scale eta, in the elapsed-time unit. | number | Required; strictly positive; finite; other constraints below |
| callerCalibratedShape | Independently calibrated positive dimensionless Weibull shape beta. | number | Required; strictly positive; finite; other constraints below |
Supply nonnegative elapsed time t and positive scale eta in the same time unit, plus positive dimensionless Weibull shape beta. Evaluate exp(-(t/eta)^beta) for a two-parameter model with zero location. t=0 returns one; a nonfinite exponent or exponential underflow to zero is rejected by the helper rather than silently returned. The tool does not fit parameters or assess model validity.
reliability=exp(-(t/eta)^beta) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Conditional two-parameter Weibull survival probability; one at elapsed time zero. | number |
{
"input": {
"elapsedTime": 2,
"callerCalibratedWeibullScale": 1,
"callerCalibratedShape": 2
},
"output": {
"result": {
"value": 0.01831563888873418
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
NIST describes the Weibull reliability model and its parameters. This calculation uses independently calibrated shape and scale with zero location rather than fitting a distribution to observed failures.2
Alternative or Complementary methods
Use MTBF Reliability Calculator for a complementary operation: A repairable-system MTBF point estimate divides operating exposure by observed failures.
Use Availability Calculator for a complementary operation: Inherent steady availability compares operating time with operating plus repair time under matched definitions.
References
Similar or alternative tools
- MTBF Reliability Calculator
A repairable-system MTBF point estimate divides operating exposure by observed failures.
- Availability Calculator
Inherent steady availability compares operating time with operating plus repair time under matched definitions.