How do you perform a Weibull probability plot, and what do the plotted values indicate?

• A. Compute F(t) and transform to ln(-ln(1−F)) vs ln t; slope gives β, intercept yields η; linear fit indicates Weibull fit.
• B. Compute F(t) and plot F(t) vs t; slope gives β.
• C. Compute F(t) and transform to log10( F ) vs log10(t); slope gives η.
• D. Compute F(t) and plot t vs 1−F; slope gives β.

Answer: (A)

Weibull probability plotting relies on linearizing the Weibull CDF so that a straight line appears if the data follow a Weibull distribution. Start with F(t), the cumulative probability of failure by time t. Transform the data by plotting y = ln(−ln(1 − F(t))) against x = ln t. For a Weibull model with shape parameter β and scale η, the CDF is F(t) = 1 − exp[−(t/η)^β]. Taking the transform gives ln(−ln(1 − F)) = β ln t − β ln η. So the plotted points should fall on a straight line whose slope is β and whose intercept is −β ln η. From the intercept you can solve for η if you know β. If the points align linearly, that indicates a good Weibull fit; if they deviate, the data may not follow a Weibull distribution or there may be censoring or other issues.