Reliability and Maintainability Fundamentals
Reliability and Maintainability Fundamentals
This domain tests the definitions and arithmetic that support every later analysis: reliability as a probability over time, failure-rate models, MTBF and MTTF, maintainability, and inherent availability. Reliability is time-dependent; a single probability without a stated mission time is meaningless.
Core rules
- R(t)=P(T>t); F(t)=1-R(t); for a constant failure rate λ, R(t)=e^(-λt) and MTBF=1/λ.
- Failure rate λ(t)=f(t)/R(t). The bathtub curve has decreasing infant mortality, a constant useful-life region, and increasing wearout.
- MTBF applies to repairable items; MTTF applies to non-repairable items. MTBF is not median life: for the exponential model, median life=0.693 MTBF.
- Maintainability M(t)=P(repair completed within t); exponential repair gives M(t)=1-e^(-μt) and MTTR=1/μ.
- Inherent availability A_i=MTBF/(MTBF+MTTR).
Worked example
A unit has λ=2×10^-5 failures/h. MTBF=1/λ=50,000 h. R(2,000 h)=e^(-(2×10^-5)(2,000))=e^(-0.04)=0.9608. With MTTR=8 h, A_i=50,000/(50,008)=0.99984. The probability of surviving to the MTBF is only e^(-1)=0.368, not 0.5, which shows why MTBF is not a median.
Traps
- Calling MTBF the average life of a wearout item.
- Mixing units, such as failures per 10^6 h versus per hour.
- Using MTTR alone for availability when logistics delay exists.
- Assuming memoryless exponential behavior when wearout is present.