Reliability Architecture: MTBF, MTTR, Series Systems and Parallel Redundancy
The equations and topology behind the Availability Architecture Lab.
Component availability
For a repairable component under the simple steady-state model, intrinsic availability is A = MTBF / (MTBF + MTTR). Increasing MTBF or reducing MTTR therefore increases modeled availability.
Topology changes the answer
For independent components required in series, system availability is the product of component availabilities. For two independent redundant components in parallel where either can satisfy the function, availability is 1 − (1−A₁)(1−A₂).
The showcase combines series dependence with a duplicated middle function to demonstrate why architecture can matter as much as an individual component metric.
Controls and interpretation
MTBF and MTTR controls alter component availability; topology determines how those component values combine. Redundancy can improve availability, but only under the independence and functional-substitution assumptions represented by the equation.
Assumptions and limits
Common-cause failures, imperfect switching, preventive maintenance, non-exponential failure behavior, logistics delay and degraded modes can invalidate the simple independent steady-state model. More detailed systems may require fault trees, Markov models or simulation.
Validation checks
Availability must remain between zero and one. Increasing MTBF with MTTR fixed must not reduce component availability. Perfect parallel redundancy cannot be less available than either independent component alone. Adding a required series component cannot improve system availability.