Calculate system reliability from component data

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Use Arc Skills to calculate system reliability from the supplied component data.

Inputs:
- Mission interval, success event and system boundary
- Component probabilities or rates with units, sources and operating conditions
- Required, redundant and shared elements, including dependencies

Return the success model, normalized inputs, intermediate equations and result scope. Identify missing factors and uncertainty. Distinguish mission reliability from availability; do not treat an unknown shared element as perfect.

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What you provide and what you get

Two required independent units yield 0.9702 for one mission

Illustrative engineering example.

In a synthetic nonrepairable mission, unit A succeeds with probability 0.99 and unit B with probability 0.98 over the same interval. Both must succeed. The numbers are illustrative mission reliabilities, not failure rates; a required shared supply exists but its reliability is unknown.

Under the stated independence and common-mission assumptions, P(A succeeds and B succeeds) = 0.99 × 0.98 = 0.9702. The path failure probability is 1 − 0.9702 = 0.0298. The 0.9702 value applies only to the two-unit path and must not be labeled complete-system reliability.

The supply is required for system success, but its reliability and dependence with A/B were not supplied. A conditional calculation or a series extension would need an explicitly justified model. This is mission reliability: it asks whether operation survives the mission without repair. Availability concerns service readiness over time and cannot be substituted for it.

Normalize before multiplying

1. Define the mission interval, success event and system boundary.
2. Check data units, operating conditions and whether values are per-mission probabilities or rates.
3. Use the architecture’s Boolean success rule with justified independence only.
4. Show intermediate arithmetic and exclusions with precision matching input quality.

Questions about this task

Can I multiply an MTBF by mission hours?

No. A rate-to-reliability conversion needs a justified failure model and consistent units; MTBF is not itself a mission success probability.

Why leave the shared supply out?

Its reliability is unknown. Treating it as perfect would overstate the complete-system result; explicitly report the bounded two-unit path instead.

Sources and further reading

• NASA Fault Tree Handbook with Aerospace Applications: NASA-hosted guidance for fault-tree gates, cut sets and reliability block diagrams.
• NASA Reliability and Maintainability: NASA overview of reliability and maintainability practice and requirements.

Related tasks

• Review a reliability block diagram: Check that the success model represents the real architecture.
• Allocate a system reliability target to subsystems: Set future subsystem targets rather than estimate current performance.
• Assess common-cause failures between redundant systems: Check whether independence assumptions hold.