Calculator inputs
Example data table
| Case | Model | Inputs | Output | Interpretation |
|---|---|---|---|---|
| Case 1 | Exponential | t = 100, λ = 0.002 | R(t) = 0.818731 | About 81.87% chance of survival. |
| Case 2 | Weibull | t = 80, β = 1.5, η = 120 | R(t) = 0.542869 | Wear-out effects lower survival probability. |
| Case 3 | Series | 0.98, 0.97, 0.99, 0.96 | R = 0.903450 | All parts must survive together. |
| Case 4 | Parallel | 0.80, 0.75, 0.85 | R = 0.992500 | Redundancy greatly improves reliability. |
| Case 5 | k-out-of-n | k = 2, n = 3, p = 0.90 | R = 0.972000 | Two working units are usually enough. |
Formula used
1) Exponential reliability
Formula: R(t) = e-λt
Meaning: Use when failure rate remains constant across time. If MTBF is known, then λ = 1 / MTBF.
2) Weibull reliability
Formula: R(t) = e-(t / η)β
Meaning: Use when systems age, improve, or show non-constant hazard. The shape parameter β controls failure behavior.
3) Series system reliability
Formula: Rseries = ∏ Ri
Meaning: Every component must work. One failure causes total system failure.
4) Parallel system reliability
Formula: Rparallel = 1 - ∏(1 - Ri)
Meaning: At least one path must work. Redundancy increases system survival probability.
5) k-out-of-n reliability
Formula: R = Σ [C(n,i) pi (1-p)n-i] for i = k to n
Meaning: The system succeeds when at least k out of n identical components work.
How to use this calculator
- Select the reliability model that matches your problem.
- Enter mission time for time-based models.
- Provide failure rate, MTBF, Weibull parameters, or component reliabilities.
- Use comma-separated values for series or parallel systems.
- Enter k, n, and component reliability for redundant identical systems.
- Press the calculate button to show the result above the form.
- Review the summary table, detailed breakdown, and Plotly graph.
- Download the visible results as CSV or PDF if needed.
FAQs
1) What does reliability probability mean?
Reliability probability is the chance that a component or system performs successfully for a required period under stated conditions. Higher values indicate lower failure risk during the mission interval.
2) When should I use the exponential model?
Use the exponential model when failure rate is constant over time. It is common for electronic parts during their useful life, where aging effects are limited.
3) Why is Weibull more flexible?
Weibull handles decreasing, constant, and increasing hazard behavior. That makes it useful for early failures, stable operation, and wear-out situations within one framework.
4) What is the difference between series and parallel systems?
In a series system, all parts must work. In a parallel system, one surviving path can keep the system operating. Parallel structures usually improve reliability through redundancy.
5) What does k-out-of-n mean?
It means the system succeeds when at least k components out of n are working. This is common in voting logic, redundant servers, and fault-tolerant hardware designs.
6) Can I enter MTBF instead of failure rate?
Yes. For the exponential model, MTBF can be converted into failure rate using λ = 1 / MTBF. The calculator performs that conversion when failure rate is left blank.
7) Why do some highly reliable components still create modest system reliability?
Series systems multiply component reliabilities together. Even strong individual values can produce a noticeably smaller overall result when many required components are included.
8) What do the CSV and PDF buttons export?
They export the current visible result section. CSV saves structured table values, while PDF captures the result block, including the table and the chart image.