\(R = P(X > Y)\) where \(X\) is the strength and \(Y\) the stress,
each Beta-Danish distributed with its own parameters.
Usage
bd_stress_strength(strength, stress, rel.tol = 1e-10)
Arguments
- strength
Named list or numeric vector giving `a`, `b`, `c`, `k` for
the strength variable \(X\).
- stress
Same, for the stress variable \(Y\).
- rel.tol
Passed to [stats::integrate()].
Value
A single probability.
Details
\(R = \int_0^\infty S_X(y) f_Y(y)\,dy\), evaluated on the Beta scale of
\(Y\) so the integral is taken over \((0,1)\).
The convention is the standard reliability one: \(R\) is the probability
that the strength exceeds the stress, so larger \(R\) means a more
reliable component. Passing the two arguments the wrong way round returns
\(1 - R\).
Examples
# Identical distributions must give one half
p <- list(a = 1.5, b = 3, c = 2, k = 1)
bd_stress_strength(strength = p, stress = p)
#> [1] 0.5
# A stronger component
bd_stress_strength(strength = list(a = 1.5, b = 3, c = 2, k = 0.5),
stress = list(a = 1.5, b = 3, c = 2, k = 2))
#> [1] 0.8723854