Calculator Form
Use the responsive calculator grid below. It displays three columns on large screens, two on smaller screens, and one on mobile devices.
Example Data Table
These examples show how different network structures change the final probability of success.
| Topology | Input Summary | Success Probability | Notes |
|---|---|---|---|
| Series | p = 0.97, n = 6 | 0.832972 | All six components must function. |
| Parallel | p = 0.82, n = 4 | 0.998950 | One functioning component is enough. |
| k-out-of-n | p = 0.88, n = 5, k = 3 | 0.985681 | At least three of five must work. |
| Path-Parallel | p = 0.95, q = 0.99, m = 3, L = 4, V = 2 | 0.991794 | Three candidate paths compete for success. |
Formula Used
1) Series Network
Formula: R = pn
All components are required. The network survives only when every component succeeds. This model is useful for chain-like systems, pipelines, or sequential communication links.
2) Parallel Network
Formula: R = 1 - (1 - p)n
Only one component needs to work. This model is useful when backup lines or redundant channels are available in parallel.
3) k-out-of-n Network
Formula: R = Σ C(n,i) pi (1-p)n-i, for i = k to n
This model counts every valid arrangement where at least k components work. It is common in voting systems, clustered servers, and threshold reliability studies.
4) Parallel Paths of Series Links
Formula: Rpath = pL qV, then R = 1 - (1 - Rpath)m
Each path contains links and optional nodes in series. The full network succeeds when at least one complete path stays operational.
How to Use This Calculator
- Select the network topology that matches your design.
- Enter the base component or link success probability p.
- Fill in the topology-specific values such as n, k, m, L, q, and V.
- Set the number of independent attempts if you want repeated-trial insights.
- Choose decimal precision for display.
- Press Calculate Probability to show the result above the form.
- Review the summary, formula, metrics, and Plotly graph.
- Use the CSV or PDF buttons to export your result.
FAQs
1) What does this calculator measure?
It measures the probability that a network or system will successfully operate under a chosen reliability structure. It also estimates repeated-attempt outcomes, sensitivity, and supporting metrics.
2) When should I use the series model?
Use the series model when every component is essential. If one part fails and the whole network stops, the series formula is the correct starting point.
3) Why is parallel reliability often higher?
Parallel systems include redundancy. The network can still work even if some components fail, so the overall success probability usually becomes much larger than a pure series design.
4) What is a k-out-of-n network?
It is a threshold system. The network succeeds when at least k out of n components operate correctly. This is useful for majority voting, clustered servers, and fault-tolerant designs.
5) What does sensitivity dR/dp mean?
Sensitivity shows how strongly the final network reliability changes when the base component probability changes slightly. Larger values mean reliability is highly responsive to component improvement.
6) What are independent attempts?
Independent attempts represent repeated uses of the same network model, such as repeated transmissions or trials. The calculator estimates the chance of at least one success and all-success performance.
7) Can I ignore nodes in the path model?
Yes. Set nodes per path to zero or keep node success probability at one. That makes the path model depend only on link reliability and path redundancy.
8) Why does the graph use changing p values?
The graph helps you see how the network behaves as the base component probability changes. It is useful for planning reliability targets and comparing design robustness.