BUILT-IN MATHEMATICA SYMBOL

ReliabilityDistribution

ReliabilityDistribution[bexpr, {{x₁, dist₁}, {x₂, dist₂}, ...}]
represents the reliability distribution for a system with components having reliability distribution , where the whole system is working when the Boolean expression bexpr is True, and component is working when is True.

Details Details

ReliabilityDistribution[bexpr, ...] corresponds to a reliability block diagram specification.
The Boolean expression bexpr is also known as the structure function for the system.
Typical structure functions include:
series system

parallel system

k-out-of-n system

BooleanConsecutiveFunction[k, n] consecutive-k-out-of-n system
The structure function bexpr can be any positive unate Boolean function.
UnateQ[bexpr] can be used to test whether a Boolean expression is positive unate.
The component reliability distributions need to be univariate with PDF[dist_i, t] and zero for t≤0.
For ReliabilityDistribution[bexpr, ...] with component indicator variables :
x_i=True indicates component working

x_i=False indicates component failed
The survival function at time t for ReliabilityDistribution[bexpr, {{x₁, dist₁}, ...}] is given by Probability[bexpr/.{x₁->t₁>t, ...}, {t₁dist_i, ...}].
ReliabilityDistribution can be used with such functions as Mean, SurvivalFunction, HazardFunction, and RandomVariate.