Hazard is instantaneous
Hazard per hour is not a cumulative probability; multiplying it by a long interval is generally wrong.
Reliability
Component Failure Distribution Calculator
Evaluate Weibull cumulative, conditional-mission, hazard, and population failure measures.
LIFE DISTRIBUTION
Translate a fitted Weibull model into age-specific service risk
For reliability engineers deciding inspection, replacement, or mission exposure for a defined component failure mode.
Mission failure risk-
Failed by current age-
Reliability at age-
Expected failed by age-
Hazard per million hours-
CURRENT DECISION RECORD
Weibull age checkpoints
Every row is regenerated from the active inputs and carried into Copy, TXT, and the page-specific PDF payload.
| Age (h) | Reliability (%) | Failed by age (%) | Expected failed units |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
F(t)=1-exp[-(t/eta)^beta]; P(t<T<=t+m | T>t)=1-R(t+m)/R(t)
Waiting for valid inputs.
HOW TO USE
From fitted life data to a mission decision
- Use failure-time data for one physical failure mode.
- Estimate Weibull shape beta and characteristic life eta outside this calculator.
- Enter current survived age and the next mission duration in hours.
- Set the exposed population to translate probability into an expected count.
- Compare conditional mission risk with cumulative risk; archive parameters and data revision.
FOUNDATIONS
Five Weibull concepts
- Shape beta
- Below one suggests decreasing hazard, one is exponential, and above one suggests increasing hazard.
- Scale eta
- Age where the two-parameter Weibull CDF reaches about 63.2%.
- Reliability R(t)
- Probability a unit survives beyond age t under the fitted mode.
- CDF F(t)
- Probability a unit has failed by age t; F(t)=1-R(t).
- Conditional mission risk
- Failure during the next mission given survival to current age.
DEEP ANALYSIS
Interpret age, hazard, and count correctly
Age changes the mission answer
With beta!=1, two identical mission lengths can carry different risks at different starting ages.
Population count is an expectation
NxF(t) supports planning but does not promise an integer field count.
CASES
Wear-out and early-life boundaries
Wear-out fleet
beta=2.2 and age near eta can make the next mission materially riskier than the same mission early in life.
Infant-mortality boundary
beta below one produces infinite theoretical hazard at t=0; use a small positive age and examine the physical fit.
TERMS
Life-data vocabulary
- Characteristic life
- Weibull scale eta.
- Cumulative hazard
- H(t)=(t/eta)^beta.
- Survival function
- Another name for reliability R(t).
- Conditional reliability
- R(t+m)/R(t).
- Censoring
- Units whose exact failure time is not observed.
- Failure mode
- A specific mechanism modeled separately.
EVIDENCE RECORD
Inputs and lineage to preserve
Archive failure-time observations, censoring flags, units, stress and environment, failure-mode definition, fitting method, beta and eta estimates, parameter uncertainty, probability plot, exclusions, and fit revision. Parameters without this lineage are not a transferable life model.
MODEL LIMITS
Where the fitted Weibull model stops
- Two-parameter Weibull with zero location only.
- Parameters are treated as known; estimation uncertainty is not propagated.
- Units are assumed identically exposed and independent.
- Competing risks, repairs, covariates, and censoring must be handled during fitting.
SOURCES
Reliability references
FAQ
Weibull distribution questions
Can beta and eta be guessed?
No. Fit them to defensible life data and retain the fitting method.
Does this include repair?
No. It is a first-failure life model for a non-repairable mode.
Why is age zero special when beta<1?
The two-parameter hazard tends to infinity at zero although cumulative failure remains finite.
Can mixed failure modes use one Weibull?
Usually not without evidence; competing modes can distort shape.
Is NxF an upper bound?
No. It is an expected count under identical independent units.
What if the fit is poor?
Use a different distribution or nonparametric estimate and do not rely on this result.
IMPORTANT LIFE-DATA NOTE
A fitted distribution is conditional evidence
Do not use the calculated age or mission probability as a certification until the failure mode, censoring, operating stress, parameter uncertainty, and Weibull fit have been reviewed for the intended population.