Calculator Inputs
Choose a basis, enter mission and adjustment factors, then calculate the unit and system failure probability.
Example Data Table
| Case | Basis | Input Summary | System Model | Failure Probability | Comment |
|---|---|---|---|---|---|
| Example 1 | Failure Rate | λ = 2.5E-5/hr, Mission = 1000 hr | Single | 2.47% | Useful for one component during a defined mission. |
| Example 2 | Failure Rate | λ = 1.2E-5/hr, Mission = 5000 hr, n = 4 | Series | 21.34% | Series systems fail when any required part fails. |
| Example 3 | Failure Rate | λ = 1.8E-5/hr, Mission = 2000 hr, n = 3 | Parallel | 0.00%–0.01% | Redundancy sharply lowers system failure probability. |
| Example 4 | MTBF | MTBF = 20000 hr, Mission = 8000 hr | Single | 32.97% | Long exposure greatly increases cumulative failure risk. |
Formula Used
These formulas assume statistically independent failures, identical components inside the selected system model, and a constant hazard rate over the mission interval.
How to Use This Calculator
- Select the calculation basis: direct failure rate, MTBF, or reference reliability.
- Choose the system model that best matches your engineering design.
- Enter mission time and the correct time unit.
- Set the number of components for series or parallel configurations.
- Apply duty cycle, environmental severity, and confidence multipliers.
- Optionally add MTTR to estimate availability along with failure probability.
- Press the calculate button to show results above the form.
- Use the CSV and PDF buttons to export the result summary.
Frequently Asked Questions
1) What does failure probability represent?
It is the chance that a component or system fails during the selected mission period. The calculator shows cumulative probability, not the instantaneous hazard at one exact moment.
2) When should I use the MTBF option?
Use MTBF when datasheets, field records, or reliability reports provide mean time between failures instead of a direct hazard rate. The calculator converts MTBF into an hourly failure rate automatically.
3) What is the difference between series and parallel models?
A series system fails if any required component fails. A parallel active redundancy system survives as long as at least one identical path remains operational. The model choice strongly changes risk.
4) Why does duty cycle affect the result?
Duty cycle reduces or increases actual exposure time. A system operating 40% of the mission accumulates less stress time than one operating continuously, so cumulative failure probability becomes lower.
5) What does the environmental severity factor do?
It adjusts the base failure rate for harsh service conditions. Values above 1 raise risk for vibration, heat, humidity, or contamination. Values near 1 reflect nominal design conditions.
6) What is the confidence multiplier for?
It lets you add conservatism when source data is uncertain. Engineers often increase the hazard rate slightly to cover model limitations, sparse field data, or design immaturity.
7) Can I start from a known reliability value?
Yes. Enter a known reliability percentage at a known reference time. The calculator converts that pair into an equivalent constant failure rate, then predicts performance over your chosen mission.
8) Are these results exact for every engineering system?
No. The results are analytical estimates based on constant hazard and independence assumptions. Complex wear-out, maintenance policies, common-cause failures, or repairable states may require deeper reliability modeling.