How this calculation works
A reliability block diagram connects component success to system success. In a series block every component must work; in an active parallel block any one successful component is sufficient under the stated model. This page combines simple internal blocks into an overall series chain. It supports mixed series and active-parallel sections without pretending to solve an arbitrary network with shared components.
Series block = product Ri; parallel block = 1−product(1−Ri); system = product block reliabilitiesA worked example
Two independent components of reliability 0.9 in an active-parallel supply block give reliability 0.99. A separate series load block with component reliabilities 0.8 and 0.5 gives 0.4. Because both blocks must work, overall reliability is 0.99 multiplied by 0.4, or 0.396. Adding redundancy to the supply cannot remove the load block’s series limitation.
Good to know
The page does not evaluate standby redundancy, imperfect switching, common-cause failure or repairable availability. Repeated use of one physical component in several rows would incorrectly count it as independent copies. The entered probabilities need their own evidence and uncertainty assessment. A clean block calculation cannot validate unreliable component data or establish a certified system safety level.
Reference: NIST — reliability modeling (opens in a new tab) ↗
What this calculation answers
A reliability block diagram connects component success to system success. In a series block every component must work; in an active parallel block any one successful component is sufficient under the stated model.
This page combines simple internal blocks into an overall series chain. It supports mixed series and active-parallel sections without pretending to solve an arbitrary network with shared components.
The Zero failure reliability demonstration sample plan calculator plans complete mission successes under a binomial model. Component reliabilities in a block model still need defensible independent evidence.
Use the right input conventions
Each record contains a block name, the word series or parallel, and space-separated reliability fractions. All fractions must describe the same mission duration and operating conditions.
Blocks themselves are connected in series. Components are assumed independent both within and between blocks; a shared power supply or common environmental failure can violate that assumption.
Interpret the result
A parallel result improves reliability mathematically because simultaneous component failure becomes the product of failure probabilities. That benefit can be overstated when the supposedly redundant components share a failure cause.
Reliability is a mission success probability here, not availability after repair. There is no repair rate, downtime or standby-switching mechanism to justify those other interpretations.
Work through the example
Two independent components of reliability 0.9 in an active-parallel supply block give reliability 0.99. A separate series load block with component reliabilities 0.8 and 0.5 gives 0.4.
Because both blocks must work, overall reliability is 0.99 multiplied by 0.4, or 0.396. Adding redundancy to the supply cannot remove the load block’s series limitation.
Where the model stops
The page does not evaluate standby redundancy, imperfect switching, common-cause failure or repairable availability. Repeated use of one physical component in several rows would incorrectly count it as independent copies.
The entered probabilities need their own evidence and uncertainty assessment. A clean block calculation cannot validate unreliable component data or establish a certified system safety level.
A few questions, answered
Are parallel components assumed to be running simultaneously?
Yes. This is active parallel redundancy, not a standby switch or repair model.
What changes in the comparison?
Replace supply redundancy with a series connection while keeping its component fractions.