The FailureProbability class

Represent a log-normal strength distribution for failure probability.

Failure is assumed to occur when load exceeds strength. All deterministic load and strength medians use the same physical unit, for example MPa.

param strength_median:

Median strength value in MPa or another consistent load unit.

type strength_median:

array_like

param strength_std:

Standard deviation of the base-10 logarithm of strength, dimensionless.

type strength_std:

array_like

Notes

For a load probability density f_L and a strength cumulative distribution F_S, the total failure probability is

\[P_f = \int_{-\infty}^{\infty} f_L(x) F_S(x)\,dx.\]

The implementation stores strengths in base-10 logarithmic space.