ReliabilityDistribution

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

This is used for reliability analysis of systems with multiple components.

Examples

(* Series system - all must work *)
ReliabilityDistribution[a && b, {{a, ExponentialDistribution[1]}, {b, ExponentialDistribution[2]}}]

(* Parallel system - at least one must work *)
ReliabilityDistribution[a || b, {{a, ExponentialDistribution[1]}, {b, ExponentialDistribution[1]}}]

Mean[ReliabilityDistribution[x1 && x2, {{x1, WeibullDistribution[2, 1]}, {x2, WeibullDistribution[2, 1]}}]]

*See the official Wolfram Language Reference for more details.