Calculator Inputs
Plotly Survival Curve
The chart displays the estimated survival curve over the selected time horizon using the adjusted constant hazard assumption.
Example Data Table
Example scenario: cohort 500, baseline hazard 0.04, hazard ratio 1.10, exposure 1.00, protection 15%, censoring 8%, horizon 12, intervals 6.
| Time | Adjusted Hazard | Survival Probability | Failure Probability | Expected Survivors |
|---|---|---|---|---|
| 2.00 | 0.037400 | 0.927927 | 0.072073 | 463.96 |
| 4.00 | 0.037400 | 0.861046 | 0.138954 | 430.52 |
| 6.00 | 0.037400 | 0.799000 | 0.201000 | 399.50 |
| 8.00 | 0.037400 | 0.741425 | 0.258575 | 370.71 |
| 10.00 | 0.037400 | 0.687998 | 0.312002 | 344.00 |
| 12.00 | 0.037400 | 0.638420 | 0.361580 | 319.21 |
Formula Used
This calculator uses a simplified constant hazard survival model. It is useful for instructional statistics, reliability studies, retention analysis, and introductory survival analysis practice.
Censoring is used here to reduce the effective cohort for a simple confidence approximation. This model assumes a constant hazard over time, so it is best treated as an educational estimator.
How to Use This Calculator
- Enter the starting cohort size.
- Provide the baseline hazard rate per time unit.
- Set the total time horizon for prediction.
- Adjust the hazard ratio for comparative risk.
- Use exposure factor to scale risk intensity.
- Enter protection percent to reduce the hazard.
- Enter censoring rate for interval estimation.
- Choose interval count for table and chart detail.
- Select a confidence level.
- Click the calculate button to view results.
- Download the table as CSV or PDF if needed.
FAQs
1. What does survival probability mean here?
It is the estimated chance that a unit, person, or observation remains event free through the selected time horizon under the model assumptions.
2. Is this a Kaplan Meier calculator?
No. This page uses a simplified constant hazard approach. It is helpful for education, rough planning, and quick scenario testing when full interval event data is unavailable.
3. What does hazard ratio change?
Hazard ratio scales the baseline hazard. Values above one increase risk. Values below one reduce risk relative to the baseline scenario.
4. Why include a protection percent?
Protection percent reduces the hazard after other risk adjustments. It can represent mitigation, shielding, treatment benefit, or any factor that lowers event intensity.
5. What is censoring rate used for?
This version uses censoring to reduce the effective cohort for approximate confidence bounds. It does not rebuild a full nonparametric survival table.
6. Can I use this for reliability studies?
Yes. The model can represent machine, component, subscription, or cohort survival when a constant hazard assumption is acceptable for the study.
7. What if the hazard is zero?
Survival remains one across time, failure stays zero, and median survival becomes infinite because the model predicts no events during the horizon.
8. Are the confidence intervals exact?
No. They are approximate instructional bounds. Use a full survival analysis workflow for research grade inference, censoring structure, and hypothesis testing.