CRE Reliability Fundamentals 2 — Questions and Answers
Question 1: A system has a constant failure rate of 0.002 failures per hour. What is the probability of surviving 100 hours of operation?
- e^(-0.2) ≈ 0.819 (Correct answer)
- e^(-0.002) ≈ 0.998
- 1 - e^(-0.2) ≈ 0.181
- 0.002 × 100 = 0.2
Correct answer: e^(-0.2) ≈ 0.819
For a constant failure rate λ, reliability R(t) = e^(-λt) = e^(-0.002×100) = e^(-0.2) ≈ 0.819.
Question 2: Which of the following best describes the 'bathtub curve' in reliability engineering?
- A plot of failure rate over time showing early failures, constant rate, and wear-out (Correct answer)
- A plot of repair rate vs. maintenance cost over a product's life
- A probability density function for normally distributed failure times
- A cumulative distribution function showing total system failures
Correct answer: A plot of failure rate over time showing early failures, constant rate, and wear-out
The bathtub curve shows three phases: infant mortality (decreasing failure rate), useful life (constant rate), and wear-out (increasing rate).
Question 3: What does the Weibull shape parameter β < 1 indicate about a failure mode?
- Infant mortality or early failures (Correct answer)
- Constant (random) failure rate
- Wear-out failures
- Fatigue-dominated failures
Correct answer: Infant mortality or early failures
A Weibull shape parameter β < 1 indicates a decreasing hazard rate, characteristic of infant mortality failures.
Question 4: Mean Time Between Failures (MTBF) is most appropriately applied to which type of system?
- Repairable systems with random failures (Correct answer)
- Non-repairable components
- Systems in the wear-out phase
- Systems with Weibull β > 1
Correct answer: Repairable systems with random failures
MTBF applies to repairable systems, representing the average time between successive failures during random-failure life.
Question 5: A reliability engineer notices that the hazard rate of a component is proportional to time (h(t) = kt). Which distribution best models this failure behavior?
- Rayleigh distribution (Correct answer)
- Exponential distribution
- Log-normal distribution
- Poisson distribution
Correct answer: Rayleigh distribution
The Rayleigh distribution (Weibull with β = 2) has a hazard rate that increases linearly with time, h(t) = t/η².
Question 6: In reliability block diagrams, what is the reliability of two components with reliabilities R₁ = 0.9 and R₂ = 0.8 connected in series?
- 0.72 (Correct answer)
- 0.98
- 0.85
- 0.10
Correct answer: 0.72
For series systems, system reliability is the product of component reliabilities: R_sys = 0.9 × 0.8 = 0.72.
Question 7: Which reliability metric measures the probability that a system will be available for use at a random point in time?
- Steady-state availability (Correct answer)
- Mission reliability
- MTTF
- Failure rate
Correct answer: Steady-state availability
Steady-state availability A = MTBF / (MTBF + MTTR) represents the long-run fraction of time a system is operational.
CRE Reliability Fundamentals 2
A system has a constant failure rate of 0.002 failures per hour.
What is the probability of surviving 100 hours of operation?