CRE CRE Statistical Methods and Reliability Modeling 1 — Questions and Answers
Question 1: Which probability distribution is most commonly used to model the time between failures for electronic components during their useful life period?
- Weibull distribution
- Exponential distribution (Correct answer)
- Normal distribution
- Lognormal distribution
Correct answer: Exponential distribution
During the useful life phase, the exponential distribution is used because it assumes a constant failure rate (λ).
Question 2: A Weibull shape parameter (β) equal to 1 indicates which type of failure behavior?
- Wear-out failures with increasing failure rate
- Infant mortality with decreasing failure rate
- Constant failure rate (random failures) (Correct answer)
- Bathtub curve pattern
Correct answer: Constant failure rate (random failures)
When β = 1, the Weibull distribution reduces to the exponential distribution, indicating a constant failure rate.
Question 3: Mean Time Between Failures (MTBF) is mathematically the reciprocal of which reliability parameter?
- System reliability R(t)
- Availability A
- Failure rate λ (Correct answer)
- Maintainability M(t)
Correct answer: Failure rate λ
MTBF = 1/λ, where λ is the constant failure rate under the exponential distribution assumption.
Question 4: A component has an MTBF of 500 hours. What is its reliability at t = 500 hours assuming an exponential distribution?
- 50.0%
- 63.2%
- 36.8% (Correct answer)
- 100.0%
Correct answer: 36.8%
R(t) = e^(-t/MTBF) = e^(-500/500) = e^(-1) ≈ 0.368 or 36.8%.
Question 5: Which reliability system model assumes that the system fails when any single component fails?
- Parallel system
- Series system (Correct answer)
- k-out-of-n system
- Active standby system
Correct answer: Series system
In a series reliability model, all components must function for the system to function, so failure of any one causes system failure.
Question 6: A Weibull shape parameter β < 1 is associated with which failure pattern in the bathtub curve?
- Wear-out failures
- Constant random failures
- Infant mortality (decreasing failure rate) (Correct answer)
- Stress-related failures
Correct answer: Infant mortality (decreasing failure rate)
β < 1 indicates a decreasing hazard rate, corresponding to early-life or infant mortality failures.
CRE CRE Statistical Methods and Reliability Modeling 1
Which probability distribution is most commonly used to model the time between failures for electronic components during their useful life period?