Calculator Inputs
Use the page as a single-column experience. The input grid expands only inside the calculator for easier data entry.
Formula Used
1) Exponential Model
Survival: S(t) = e-λt
Failure: F(t) = 1 - S(t)
Cumulative hazard: H(t) = λt
This model assumes a constant hazard rate across time.
2) Weibull Model
Survival: S(t) = e-(t/η)β
Hazard: h(t) = (β/η)(t/η)β-1
Use Weibull when hazard rises or falls over time.
3) Discrete Interval Model
Survival: S(t) = pt/Δt
Approximate hazard: h ≈ -ln(p)/Δt
This works well for cycle-based decisions and repeated checks.
4) Kaplan–Meier Model
Product-limit survival: S(t) = ∏ (1 - di/ni)
Confidence support: Greenwood variance is used for interval estimation.
Choose this for observed event data with censoring.
Confidence Interval Logic
Parametric modes use an approximate Wilson interval for survival at the chosen time. Kaplan–Meier mode uses a log-log style interval based on Greenwood’s variance accumulation.
How to Use This Calculator
- Select the model that best matches your data.
- Enter a time horizon and chart step size.
- Fill in the method-specific fields.
- Set a target survival percentage for decision timing.
- Choose confidence level and decimal precision.
- Click the calculate button.
- Review the result cards, detailed table, and Plotly graph.
- Export the generated results as CSV or PDF.
Example Data Table
| Model | Inputs | Time | Survival | Failure | Median Life | Mean or Restricted Mean |
|---|---|---|---|---|---|---|
| Exponential | λ = 0.08 | 10 | 0.4493 | 0.5507 | 8.6643 | 12.5000 |
| Weibull | η = 15, β = 1.5 | 10 | 0.5802 | 0.4198 | 11.7483 | 13.5412 |
| Discrete | p = 0.94, Δt = 1 | 10 | 0.5386 | 0.4614 | 11.2023 | 16.6667 |
| Kaplan–Meier | Example rows in textarea | 6 | Computed from cohort | Computed from cohort | First time S(t) ≤ 0.50 | Restricted to observed horizon |
These rows are illustrative and help verify your first run.
FAQs
1) What does survivability mean here?
It means the probability that a subject, system, patient, device, or process remains event-free up to a chosen time horizon.
2) Which model should I choose first?
Use Kaplan–Meier for observed cohort data, exponential for constant hazard assumptions, Weibull for changing hazard, and discrete mode for cycle-based survival.
3) Why is Weibull often preferred?
Weibull can represent increasing, decreasing, or constant hazard patterns, so it fits many real reliability and risk situations better than a constant-rate model.
4) What is censoring in Kaplan–Meier?
Censoring means an item leaves observation without the event being observed. The method keeps that information without treating it as a failure.
5) Is the confidence interval exact?
No. Parametric modes use an approximate interval around the survival estimate. Kaplan–Meier mode uses a standard variance-based approximation.
6) What does cumulative hazard show?
It summarizes total risk accumulation over time. Higher cumulative hazard means more exposure to the event by the selected horizon.
7) Why might target time show N/A?
That happens when the curve never falls to your chosen target survival level within observed or modeled time.
8) Can I use this for medicine and engineering?
Yes. The calculator is general and supports medical follow-up, reliability studies, maintenance planning, operational continuity, and many other statistical survival tasks.