CMRP Reliability Data Analysis and Statistics 1 — Questions and Answers
Question 1: What does MTBF stand for in reliability engineering?
- Mean Time Between Failures (Correct answer)
- Maximum Time Before Failure
- Mean Total Breakdown Frequency
- Minimum Threshold for Basic Function
Correct answer: Mean Time Between Failures
MTBF (Mean Time Between Failures) is the average time between successive failures of a repairable system and is a foundational reliability metric.
Question 2: Which formula correctly calculates failure rate (λ) from MTBF?
- λ = MTBF × Number of failures
- λ = 1 / MTBF (Correct answer)
- λ = MTBF + MTTR
- λ = Number of failures / MTBF
Correct answer: λ = 1 / MTBF
Failure rate (λ) equals 1/MTBF, representing the frequency of failures per unit of operating time.
Question 3: What does the bathtub curve illustrate in reliability engineering?
- The relationship between maintenance cost and equipment age
- The failure rate pattern showing infant mortality, constant rate, and wear-out phases (Correct answer)
- The optimal frequency for preventive maintenance intervals
- The cumulative distribution function of repair times
Correct answer: The failure rate pattern showing infant mortality, constant rate, and wear-out phases
The bathtub curve describes the three phases of equipment life: infant mortality (decreasing failure rate), useful life (constant rate), and wear-out (increasing failure rate).
Question 4: What is 'censored data' in the context of reliability analysis?
- Data that has been filtered to remove outliers
- Data from units that have not failed or were removed before failure (Correct answer)
- Data collected under accelerated test conditions
- Data restricted by regulatory confidentiality requirements
Correct answer: Data from units that have not failed or were removed before failure
Censored (suspended) data represents units that have not yet failed or were removed from service before failure, requiring special statistical methods for inclusion in reliability calculations.
Question 5: If a pump has an MTBF of 2,000 hours and an MTTR of 8 hours, what is its inherent availability?
- 99.0%
- 99.6% (Correct answer)
- 97.5%
- 98.4%
Correct answer: 99.6%
Availability = MTBF / (MTBF + MTTR) = 2000 / (2000 + 8) = 2000 / 2008 ≈ 0.996 or 99.6%.
Question 6: Reliability is formally defined as the probability that a system performs its required function for a specified period under which conditions?
- Under ideal laboratory conditions only
- Under the worst-case operating conditions
- Under stated conditions for a specified time interval (Correct answer)
- Under average field operating conditions
Correct answer: Under stated conditions for a specified time interval
Reliability is the probability that an item performs its required function under given (stated) conditions for a specified time interval, per IEEE and IEC standards.
Question 7: For a component following the exponential distribution with an MTBF of 500 hours, what is its reliability at t = 500 hours?
- 50.0%
- 63.2%
- 36.8% (Correct answer)
- 100%
Correct answer: 36.8%
For exponential distribution, R(t) = e^(-t/MTBF); at t = MTBF, R = e^(-1) ≈ 0.368 or 36.8%.
CMRP Reliability Data Analysis and Statistics 1
What does MTBF stand for in reliability engineering?