Mission Reliability Calculator R(t)

That ~1 in 12 such missions ends in an unplanned failure — so for 50 campaigns a year, budget ~4 failure events: spares, intervention crews, schedule slack. R(t) converts reliability from a feeling into a frequency you can provision against. If the consequence of failure is severe, either shorten the mission (mid-campaign service), raise MTBF, or add redundancy.

The exponential model assumes a constant failure rate — the flat middle of the bathtub curve — where failures arrive randomly regardless of age. It's a good approximation for electronics in mid-life and complex repairable systems, and a poor one during infant mortality or wear-out. If your failures cluster with age, fit a Weibull (shape β>1 means wear-out) instead of using this simple model.

Multiply the individual R(t) values if failures are independent: R_line = R₁ × R₂ × … . Series chains erode brutally (ten 99% units → 90.4%), parallel redundancy rescues: two parallel units each with R = 0.92 give 1 − (0.08)² ≈ 99.4% if either alone can carry the load. This is the math behind N+1 design.

Yes, reframed: with a fleet of n units each having reliability R(t) for the mission, the expected number of failures is n × (1 − R(t)) and the probability of zero fleet failures is R(t)ⁿ. Twenty trucks at 95% weekly reliability → expect one failure per week (20 × 0.05) and only a 36% chance of a failure-free week. Plan the workshop accordingly.