CRE Life Data Analysis 3 — Questions and Answers
Question 1: In accelerated life testing (ALT) data analysis, the Arrhenius model relates failure acceleration to:
- Applied mechanical stress
- Temperature in Kelvin (Correct answer)
- Voltage or electrical stress
- Vibration frequency
Correct answer: Temperature in Kelvin
The Arrhenius model uses absolute temperature (Kelvin) and an activation energy to model thermally-driven acceleration of failure rates.
Question 2: A Weibull probability plot shows data points curving upward (concave up) rather than forming a straight line. This most likely indicates:
- A mixed population or two failure modes (Correct answer)
- The exponential distribution fits better
- The shape parameter β is exactly 1
- Data collection errors only
Correct answer: A mixed population or two failure modes
Upward curvature on a Weibull plot often signals a mixed (competing) failure mode population, where two distinct subpopulations are present.
Question 3: The B10 life of a component refers to the time by which:
- 90% of units have failed
- 50% of units have failed
- 10% of units have failed (Correct answer)
- 1% of units have failed
Correct answer: 10% of units have failed
BX life (here B10) is the time at which X% of the population has failed, so B10 is the 10th-percentile failure time.
Question 4: Maximum Likelihood Estimation (MLE) is preferred over rank regression for life data analysis primarily because:
- It always gives lower parameter estimates
- It handles censored data more rigorously and is asymptotically efficient (Correct answer)
- It requires no assumptions about the failure distribution
- It produces exact confidence intervals for small samples
Correct answer: It handles censored data more rigorously and is asymptotically efficient
MLE properly incorporates censored observations into the likelihood function and achieves the Cramér-Rao lower bound efficiency for large samples.
Question 5: For a 3-parameter Weibull distribution, the third parameter γ (gamma) represents:
- The characteristic life
- The shape of the hazard function
- A guaranteed failure-free (location) period (Correct answer)
- The mean life of the population
Correct answer: A guaranteed failure-free (location) period
The location parameter γ shifts the distribution so that no failures can occur before time γ, representing a failure-free period.
Question 6: When computing failure rates from field warranty data, a major challenge compared to controlled test data is:
- Too few failure events are recorded
- Exact time-in-service for all units is typically unknown (Correct answer)
- Warranty data cannot be right-censored
- The Weibull distribution does not apply to warranty data
Correct answer: Exact time-in-service for all units is typically unknown
Warranty data rarely includes precise in-service hours for non-failed units, making suspension times uncertain and requiring special analysis methods.
Question 7: The hazard function h(t) for an exponential distribution with failure rate λ is:
- λ·t
- λ·e^(−λt)
- λ (Correct answer)
- 1 − e^(−λt)
Correct answer: λ
The exponential distribution has a constant hazard rate h(t) = λ for all t, reflecting the memoryless property.
CRE Life Data Analysis 3
In accelerated life testing (ALT) data analysis, the Arrhenius model relates failure acceleration to: