CET Follow-Up & Survival Analysis 3 — Questions and Answers
Question 1: In the Weibull distribution, a shape parameter β > 1 indicates:
- Decreasing failure rate (infant mortality)
- Constant failure rate
- Increasing failure rate (wear-out) (Correct answer)
- A log-normal failure pattern
Correct answer: Increasing failure rate (wear-out)
When β > 1, the Weibull hazard function increases over time, which is characteristic of wear-out failures.
Question 2: What does the scale parameter η (eta) represent in the Weibull distribution?
- The minimum guaranteed life of the component
- The time at which exactly 63.2% of units have failed (Correct answer)
- The slope of the Weibull probability plot
- The median life of the population
Correct answer: The time at which exactly 63.2% of units have failed
η is the characteristic life; at t = η, the cumulative failure fraction is always 1 − 1/e ≈ 63.2% regardless of β.
Question 3: When β = 1 in the Weibull distribution, it simplifies to which distribution?
- Normal distribution
- Log-normal distribution
- Poisson distribution
- Exponential distribution (Correct answer)
Correct answer: Exponential distribution
At β = 1, the Weibull hazard function becomes constant, making it identical to the exponential distribution.
Question 4: On a Weibull probability plot, the slope of the best-fit line estimates which parameter?
- The scale parameter η
- The location parameter γ
- The shape parameter β (Correct answer)
- The MTBF
Correct answer: The shape parameter β
The slope of the line on a Weibull probability plot directly estimates the shape parameter β.
Question 5: The cumulative hazard function H(t) is related to the survival function S(t) by:
- H(t) = S(t)
- H(t) = 1 − S(t)
- H(t) = ln[S(t)]
- H(t) = −ln[S(t)] (Correct answer)
Correct answer: H(t) = −ln[S(t)]
By definition S(t) = e^(−H(t)), so rearranging gives H(t) = −ln[S(t)].
Question 6: Which test is most commonly used to compare the survival curves of two independent groups?
- Paired t-test
- Log-rank test (Correct answer)
- Chi-square goodness-of-fit
- Analysis of variance (ANOVA)
Correct answer: Log-rank test
The log-rank test compares overall survival distributions between groups and handles censored data correctly.
Question 7: In a reliability block diagram, series-connected components produce a system reliability that is:
- Equal to the highest individual component reliability
- Greater than all individual component reliabilities
- Less than the lowest individual component reliability (Correct answer)
- Equal to the product of component reliabilities divided by the number of components
Correct answer: Less than the lowest individual component reliability
All series components must work simultaneously, so the system reliability is the product of individual reliabilities and is lower than any single component.
CET Follow-Up & Survival Analysis 3
In the Weibull distribution, a shape parameter β > 1 indicates: