CET Follow-Up & Survival Analysis 3

Question 1

In the Weibull distribution, a shape parameter β > 1 indicates:

Accepted Answer

Increasing failure rate (wear-out)

Answer

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?

Accepted Answer

The time at which exactly 63.2% of units have failed

Answer

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?

Accepted Answer

Exponential distribution

Answer

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?

Accepted Answer

The shape parameter β

Answer

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:

Accepted Answer

H(t) = −ln[S(t)]

Answer

By definition S(t) = e^(−H(t)), so rearranging gives H(t) = −ln[S(t)].

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