CET Follow-Up & Survival Analysis 2 — Questions and Answers
Question 1: What does the survival function S(t) represent in reliability analysis?
- The instantaneous failure rate at time t
- The probability that a component survives beyond time t (Correct answer)
- The cumulative number of failures up to time t
- The average time between failures
Correct answer: The probability that a component survives beyond time t
S(t) gives the probability that a component or system has not failed by time t.
Question 2: If a component has a constant failure rate λ = 0.002 failures/hour, what is its MTBF?
- 200 hours
- 2,000 hours
- 500 hours (Correct answer)
- 50 hours
Correct answer: 500 hours
MTBF = 1/λ = 1/0.002 = 500 hours for a constant (exponential) failure rate.
Question 3: In the 'bathtub curve,' which region is characterized by a decreasing failure rate?
- Useful life period
- Wear-out period
- Random failure period
- Infant mortality period (Correct answer)
Correct answer: Infant mortality period
The infant mortality (early failure) region shows a decreasing failure rate as weak units are screened out.
Question 4: The hazard function h(t) in reliability analysis represents:
- The total cumulative failures over time
- The probability of surviving past time t
- The instantaneous failure rate given that the item has survived to time t (Correct answer)
- The mean number of failures per unit time
Correct answer: The instantaneous failure rate given that the item has survived to time t
h(t) is the conditional instantaneous failure rate for units that have survived up to time t.
Question 5: What is 'right censoring' in a survival analysis context?
- Removing outlier failure times from the dataset
- Observing a failure that occurs before the study ends
- The study ending before all items have failed (Correct answer)
- Truncating data below a minimum threshold
Correct answer: The study ending before all items have failed
Right censoring occurs when the observation period ends before a unit fails, so the exact failure time is unknown but known to be beyond the observation time.
Question 6: The Kaplan-Meier estimator is primarily used to:
- Calculate the Weibull shape parameter β
- Estimate the survival function nonparametrically from censored data (Correct answer)
- Fit an exponential distribution to failure times
- Determine the acceleration factor in ALT
Correct answer: Estimate the survival function nonparametrically from censored data
The Kaplan-Meier method estimates the empirical survival function and correctly handles censored observations.
Question 7: The exponential reliability model assumes which type of failure rate?
- Increasing failure rate over time
- Decreasing failure rate over time
- Constant failure rate (memoryless property) (Correct answer)
- Bathtub-shaped failure rate
Correct answer: Constant failure rate (memoryless property)
The exponential distribution's defining property is a constant hazard rate, which makes past operating time irrelevant to future failure probability.
CET Follow-Up & Survival Analysis 2
What does the survival function S(t) represent in reliability analysis?