Life Data Analysis Flashcards

In Weibull analysis, a shape parameter (β) of exactly 1 indicates which failure behavior?

Answer: Constant failure rate (random failures)

When β = 1, the Weibull distribution reduces to the exponential distribution, which has a constant (memoryless) failure rate.

Which method for parameter estimation minimizes the sum of squared deviations between observed and predicted reliability values on a probability plot?

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.

A suspended (censored) test item in life data analysis is one that:

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.

The median rank formula (Benard's approximation) for the i-th failure out of n units is:

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.

In a lognormal life distribution, the parameter σ (log-standard deviation) primarily controls:

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.

When analyzing interval-censored life data, each unit's failure time is known to fall:

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.

Which goodness-of-fit statistic is most commonly used to assess how well a Weibull model fits life data on a probability plot?

Answer: Correlation coefficient (ρ)

The correlation coefficient ρ measures linearity on the Weibull probability plot; values close to 1 indicate a good fit.