Reliability Testing and Demonstration
Reliability Testing and Demonstration
This domain tests how tests prove reliability with confidence: success-run tests, MTBF demonstration, sequential testing, and the difference between demonstrated and predicted values.
Core rules
- Zero-failure binomial test: n=ln(1-C)/ln(R), where C is confidence and R is the reliability to demonstrate.
- Zero-failure exponential time test: T=-MTBF_target ln(1-C).
- The sequential probability ratio test compares H0: MTBF=θ0 with H1: MTBF=θ1 using producer risk α and consumer risk β; it requires a pre-agreed discrimination ratio.
- Test conditions must match the use environment. Acceleration requires a validated model relating stress to life.
Worked example
Demonstrate R=0.95 at 90% confidence with zero failures: n=ln(0.10)/ln(0.95)=-2.3026/-0.05129=44.9, so 45 units with no failures. For an MTBF goal of 1,000 h at 80% confidence and zero failures: T=-1,000 ln(0.20)=1,609 h of test time. One failure changes the calculation and requires the full binomial or sequential method.
Traps
- Reporting 90% confidence as 90% reliability.
- Using the success-run formula after failures occur.
- Treating demonstrated MTBF as the true MTBF.
- Testing at unrealistic stress without an acceleration model.