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Parallel System Reliability Calculator

Calculate system success probability for 2–100 independent parallel paths, with different reliability values if needed. At least one path must complete the required function for the same mission duration.

Parallel-path reliabilities

Enter probabilities from 0 to 1, not percentages. Set the path count, apply it, then enter every path. New paths start blank.

https://reliabilitybench.com/tools/parallel-system-reliability-calculator.html
Independent paths; at least one operates; all inputs use the same mission duration. Shared failures, repairs, switching failures, and load sharing are excluded.

What this calculator does

The tool calculates the probability that at least one path operates by subtracting the probability that every path fails. It accepts two to 100 independent paths, including unequal reliabilities. Results include the all-path failure probability and the percentage-point gain over the most reliable single path.

When to use it

Use it for an active parallel reliability block where any one path can perform the full required duty. Evaluate all paths over the same mission duration and operating conditions. Use the K-out-of-N calculator if more than one identical component must operate.

Inputs and formula

Enter each path's mission reliability as a probability: 0.90 means 90%. A value of zero represents a path that cannot succeed in the modeled mission. A value of one asserts certainty under the model. Blank inputs are rejected.

Qsystem = ∏ (1 − Ri); Rsystem = 1 − Qsystem

The product runs over all entered paths. Gain over the best single path is 100 × (Rsystem − max Ri) percentage points. For high reliabilities, inspect the failure probability: a displayed approximately 100% does not mean failure is impossible.

Worked example and interpretation

Two paths with reliabilities 0.90 and 0.80 have an all-path failure probability of 0.10 × 0.20 = 0.02. System reliability is 98%, a gain of 8 percentage points over the 90% single path. Adding an independent 0.70 path reduces failure probability to 0.6% and raises reliability to 99.4%.

Set the path count to 2 and apply it to reproduce the two-path example. Existing leading inputs are retained when the count changes. Reset restores the three-path sample and clears the previous result.

Practical notes and limitations

Independence is essential. Common utilities, maintenance errors, software, environment, and shared demand can disable multiple paths together. The calculated gain applies only to the entered independent-path model. It is not a recommendation to add equipment.

Standby starts, switching failures, changing load after a failure, repairs during the mission, and common-cause failures require a different model. Mission reliability is not repairable-system availability or MTBF. A path may itself be a series subsystem, but its input must already represent that complete path's reliability.

Inputs stay in your browser. Copy and Print include the calculated inputs, units, results, assumptions, and page URL. Editing an input clears the result until you calculate again.

Method source

NIST/SEMATECH e-Handbook: Parallel or redundant model defines independent paths and the product of component failure probabilities.

Series systemK-out-of-N reliabilityReliability block diagramsAvailabilityFormula reference