Series and Parallel System Reliability Calculator
A reliability block diagram turns a design into arithmetic. This calculator handles the most common case: a chain of blocks in series where one block is duplicated for redundancy.
Your numbers
Probability block 1 works for the mission.
Usually the weakest block.
Your results
Assumes independent failures and perfect switching for active redundancy. Common cause failures and switch failure reduce real gains.
System reliability (%) vs block 3 single-unit reliability
Sweeps Block 3 reliability (single unit) from 50 to 99.9, holding your other inputs fixed.
Design reliability review
Optional discussion on linking reliability predictions with field data in your systems.
Optional. The tool and every export work without this. No spam.
How to use the calculator
Enter the mission reliability for each of three blocks, then choose how many identical units run in parallel for block 3. The calculator shows the system reliability with and without redundancy and the gain. Use it during DFMEA work to see which block deserves a design change, or to test whether redundancy is worth the added cost and weight.
The formulas
Series blocks all must work, so system reliability is the product of the block reliabilities. For n identical units in active parallel, the block works if at least one unit works, giving R = 1 minus (1 minus r) to the power n. The system then multiplies the effective block 3 value with blocks 1 and 2. Three 95 percent blocks in series give about 85.7 percent, which surprises many teams.
- Series: reliability always falls as blocks are added.
- Parallel: gains shrink quickly after two or three units.
Reading the result
The gain output shows how much the redundancy buys in percentage points. If the system is still limited by block 1 or 2 after redundancy, the lowest-block output tells you where to look next. Redundancy lowers the severity of single faults but does not remove the cause, so keep the corresponding DFMEA rows open.
Common mistakes
Assuming independence is the main error. A shared power supply, common software or the same environment can fail redundant units together. Also, a standby arrangement needs switch reliability in the calculation, which this simple active model ignores. Finally, make sure every block uses the same mission time.
Frequently Asked Questions
What is active parallel redundancy?
All units run at the same time and the block succeeds if at least one survives. Standby redundancy keeps spares idle and needs a switching model.
Why is the chart showing two lines?
One line is the system without redundancy and the other with it. The gap between them is the benefit, which is largest when the single unit is weak.
Can I use MTBF values?
Convert them first: reliability for a mission time t is exp(-t/MTBF) for constant failure rate. The FIT and MTBF converter on this site does that.
How many parallel units are sensible?
Usually two. A third adds little unless single-unit reliability is low or the consequence of failure is severe.
Netray can help tie design reliability assumptions to observed field failures held in your ERP and service systems.
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