Network reliability evaluation

Example 1: five‐node/two‐path static network.

Fifty‐two node Weibull results graphical comparison.

Example 14: 52‐node Weibull network, s = 1, t = 52.

Nineteen‐node Weibull results for graphical comparison.

Linear graph for 1/α.

Linear graph for β.

Exponential graph for β.

Example 13: 19‐node Weibull network.

Weibull reliability distributions.

Example 12: implementation of multistate overlap reliability to 52‐node network in 18 s. Solution (s = 1, t = 52): full reliability = 0.05, derated reliability = 0.51, full unreliability = 0.44.

Example 11: implementation of multistate overlap reliability to 19‐node network in 1.26 s. Solution (s = 1, t = 19): full reliability = 0.36, derated reliability = 0.43, full unreliability = 0.21.

Example 10: power plant with four multiple derated turbines (nodes 1 to 4) in parallel and a transformer (egress node 5) in series, and node 0 (as an ingress dummy node with full reliability).

Example 9: active parallel–series system with doubly derated states for 2 and 3.

Example 8: a simple parallel–series system with single derated states.

Example 7: active parallel system with IN(1) and OUT(4) full reliability; others(2,3) are derated.

Example 6: simple series system with a derated state.

Example 5: Simulation for (s = 1, t = 52) with 72 links is 0.558 in 17,119 s. The faster analytical result is 0.556 in 18.034 s in 0.1% of the much longer simulation time. The more simulation runs are conducted, the closer the analytical and simulation results will converge to each other.

Example 4: 19‐node (s = 1, t = 19) complex network with Monte Carlo simulation (83 s) and analytical results (50 s), both 0.784 with simulation taking 33 s more.

Example 3: eight‐node/nine‐path static network with s = 7, t = 8.

Example 2: six‐node network without including link reliabilities ( = 1.0) and (s=1, t=6) solution.