CRE Life Data Analysis 2 — Questions and Answers
Question 1: In Weibull analysis, a shape parameter (β) of exactly 1 indicates which failure behavior?
- Increasing failure rate (wear-out)
- Constant failure rate (random failures) (Correct answer)
- Decreasing failure rate (infant mortality)
- Bathtub-shaped failure rate
Correct answer: Constant failure rate (random failures)
When β = 1, the Weibull distribution reduces to the exponential distribution, which has a constant (memoryless) failure rate.
Question 2: Which method for parameter estimation minimizes the sum of squared deviations between observed and predicted reliability values on a probability plot?
- Maximum Likelihood Estimation (MLE)
- Method of Moments
- Rank Regression on X (RRX) (Correct answer)
- Bayesian estimation
Correct answer: Rank Regression on X (RRX)
Rank Regression on X (RRX) fits parameters by minimizing the horizontal (X-axis) squared residuals on a Weibull probability plot.
Question 3: A suspended (censored) test item in life data analysis is one that:
- Failed at a known time
- Was removed from test without failing (Correct answer)
- Failed at an unknown time
- Failed due to a competing failure mode
Correct answer: Was removed from test without failing
Suspended (right-censored) units are items removed from the test before failure, providing only a lower bound on their true failure time.
Question 4: The median rank formula (Benard's approximation) for the i-th failure out of n units is:
- (i − 0.3) / (n + 0.4) (Correct answer)
- (i − 0.5) / n
- i / (n + 1)
- (i − 0.7) / (n + 0.4)
Correct answer: (i − 0.3) / (n + 0.4)
Benard's approximation for median ranks is F(i) ≈ (i − 0.3) / (n + 0.4), widely used for Weibull probability plotting.
Question 5: In a lognormal life distribution, the parameter σ (log-standard deviation) primarily controls:
- The location (median) of the distribution
- The spread or dispersion of the distribution (Correct answer)
- The minimum possible failure time
- The maximum failure rate
Correct answer: The spread or dispersion of the distribution
In the lognormal distribution, σ is the scale parameter governing spread; a larger σ means greater variability in failure times.
Question 6: When analyzing interval-censored life data, each unit's failure time is known to fall:
- Exactly at the recorded time
- Before the recorded inspection time
- Between two inspection times (Correct answer)
- After all other failures
Correct answer: Between two inspection times
Interval-censored data occurs when inspection is periodic and failure is only known to have occurred between the last passing and first failing inspection.
Question 7: Which goodness-of-fit statistic is most commonly used to assess how well a Weibull model fits life data on a probability plot?
- Kolmogorov-Smirnov statistic
- Correlation coefficient (ρ) (Correct answer)
- Chi-squared statistic
- Anderson-Darling statistic
Correct answer: Correlation coefficient (ρ)
The correlation coefficient ρ measures linearity on the Weibull probability plot; values close to 1 indicate a good fit.
CRE Life Data Analysis 2
In Weibull analysis, a shape parameter (β) of exactly 1 indicates which failure behavior?