The FailureProbability class

Strength representation to calculate failure probabilities

The strength is represented as a log normal distribution of strength_median and strength_std.

Failure probabilities can be calculated for a given load or load distribution.

param strength_median

The median value of the strength

type strength_median

array_like, shape (N, )

param strength_std

The standard deviation of the strength

type strength_std

array_like, shape (N, )

Note

We assume that the load and the strength are statistically distributed values. In case the load is higher than the strength we get failure. So if we consider a quantile of our load distribution of a probability p_load, the probability of failure due to a load of this quantile is p_load times the probability that the strength lies within this quantile or below.

So in order to calculate the total failure probability, we need to integrate the load’s pdf times the strength’ cdf from -inf to +inf.