Model component success, mission time, and redundancy. See probabilities, charts, tables, exports, and importance measures. Make stronger reliability decisions using transparent calculations and visuals.
Use direct reliability values or convert failure rates over mission time. The form stays in one stacked page, while fields arrange in 3, 2, or 1 columns by screen width.
| Branch | Reliability | Failure Probability |
|---|---|---|
| Branch A | 0.9200 | 0.0800 |
| Branch B | 0.8900 | 0.1100 |
| Branch C | 0.9500 | 0.0500 |
| Branch D | 0.9000 | 0.1000 |
| System | 0.999956 | 0.000044 |
Example formula: 1 − [(1−0.92)(1−0.89)(1−0.95)(1−0.90)] = 0.999956.
Direct branch reliability: Ri = entered branch reliability
From failure rate and mission time: Ri(t) = e−λit
Parallel system reliability: Rparallel = 1 − ∏(1 − Ri)
Parallel system failure probability: Qparallel = ∏(1 − Ri)
Branch importance at current point: Ii = ∏j≠i(1 − Rj)
A parallel system succeeds when at least one independent branch succeeds. That is why total reliability is found by subtracting the probability of all branches failing from one.
If you choose failure-rate mode, each branch reliability is first converted with the exponential model. This is common when failures follow a constant hazard assumption.
It uses R = 1 − ∏(1 − Rᵢ). The system works if at least one independent branch works, so total failure happens only when every branch fails together.
Redundancy improves performance. In a true parallel arrangement, one successful branch can keep the system working, so the combined reliability usually exceeds any individual branch reliability.
Yes. Choose failure-rate mode, enter a mission time, and the calculator converts each branch with R(t) = e^(−λt) before combining them into the final system result.
The main assumptions are independent branch failures and active parallel operation. In rate mode, the exponential reliability model also assumes a constant hazard rate over the mission interval.
Yes. If all branches are identical, enter the same reliability or failure rate for each branch. The calculator still uses the same parallel reliability structure and gives the correct combined result.
It shows how sensitive total system reliability is to each branch at the current operating point. Larger values mean that branch contributes more strongly to the final redundancy benefit.
Not exactly. This page is for active parallel branches. Standby systems usually need switching logic, coverage assumptions, and different state-based reliability modeling.
It is back-calculated from the final reliability over the entered mission interval. Changing the mission time changes the equivalent rate needed to represent that same reliability level.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.