Backup Power for Nuclear Power Plants
Backup Power for Nuclear Power Plants
Calculate basic reliability properties for a backup diesel generator.
bexprEDG = (e110 && ((e107 && (e103 || e104 || e99 || e89 || e98 || e91 || e101 || e105 || e4 || e111 || e95)) || (e5 && (e103 || e104 || e99 || e89 || e98 || e91 || e101 || e105 || e93) && (e100 || e90 || e97 || e102 || e92 || e108 || e107)) || ((e7 || e12 || e9) && (e103 || e104 || e99 || e89 || e98 || e91 || e101 || e105 || e4 || ((e111 || e95) && e121))))) || (e109 && ((e104 && (e106 || e107 || e100 || e90 || e97 || e102 || e92 || e108 || e4 || e111 || e96)) || ((e106 || e107 || e100 || e90 || e97 || e102 || e92 || e108 || e94) && e5 && (e99 || e89 || e98 || e91 || e101 || e105 || e104)) || ((e6 || e11 || e8) && (e106 || e107 || e100 || e90 || e97 || e102 || e92 || e108 || e4 || ((e111 || e96) && e121))))) || ((e5 || e88) && (e85 || e87 || e84 || e81 || e80 || e83)) || e82 || e86 || e16 || e29 || e14 || e66 || e18 || e26 || ((e120 || e113 || e112 || e116 || e118 || e115 || e114 || e117 || e4) && e5) || e119 || e27 || e10 || e25 || e17 || e73 || e78 || e74 || e79 || e76 || e72 || e77 || ((e56 || e55 || e53 || e19) && (e58 || e57 || e54 || e20)) || e70 || e71 || e28 || e15 || e64 || e65 || e67 || e46 || e45 || e36 || e22 || e47 || e49 || e48 || e37 || e23 || e50 || e42 || e40 || e41 || e43 || e21 || e61 || e33 || ((e59 || e32) && (e63 || e35)) || e38 || e69 || e68 || e39 || e13 || e62 || e34 || e31 || e24 || e60 || e30 || e51 || e75 || e52;distsEDG = Map[{#[[1]], ExponentialDistribution[#[[2]]]}&, {{e99, (2/10^4)}, {e89, (3.38/10^4)}, {e98, (2/10^4)}, {e91, (3.38/10^4)}, {e101, (4/10^3)}, {e105, (2.4/10^3)}, {e103, (1.1/10^2)}, {e104, (3.2/10^5)}, {e111, (2/10^4)}, {e95, (1.35/10^4)}, {e100, (2/10^4)}, {e90, (3.38/10^4)}, {e97, (2/10^4)}, {e102, (4/10^3)}, {e92, (3.38/10^4)}, {e108, (2.4/10^3)}, {e106, (9/10^4)}, {e107, (3.2/10^5)}, {e16, (1.52/10^6)}, {e29, (2/10^7)}, {e26, (2/10^7)}, {e14, (1.52/10^6)}, {e66, (1.2/10^6)}, {e18, (1.52/10^6)}, {e72, (1.52/10^6)}, {e77, (2/10^7)}, {e74, (1.52/10^6)}, {e79, (5/10^4)}, {e1, (7/10^6)}, {e2, (1.52/10^6)}, {e3, (1.52/10^6)}, {e76, (2/10^7)}, {e4, (2/10^7)}, {e93, (1.35/10^4)}, {e5, 1}, {e96, (1.35/10^4)}, {e94, (1.35/10^4)}, {e109, 1}, {e85, (2/10^3)}, {e87, (4.84/10^4)}, {e84, (2/10^4)}, {e81, (2/10^3)}, {e80, (3.38/10^4)}, {e83, (4.84/10^4)}, {e88, 1}, {e82, (7.89/10^6)}, {e86, (7.89/10^6)}, {e121, 1}, {e7, (8.48/10^8)}, {e12, (3.2/10^5)}, {e9, (1.4/10^7)}, {e120, (2.4/10^3)}, {e113, (2/10^4)}, {e112, (2/10^4)}, {e116, (4/10^3)}, {e118, (2.4/10^3)}, {e115, (2/10^4)}, {e114, (2/10^4)}, {e117, (4/10^3)}, {e110, 1}, {e6, (8.48/10^8)}, {e8, (1.4/10^7)}, {e11, (8.48/10^8)}, {e10, (3.2/10^5)}, {e27, (2/10^7)}, {e119, (3.2/10^5)}, {e28, (2/10^7)}, {e15, (1.52/10^6)}, {e58, (2/10^3)}, {e57, (2.5/10^5)}, {e54, (1/10^5)}, {e20, (3.38/10^4)}, {e56, (2/10^3)}, {e55, (2.5/10^5)}, {e53, (1/10^5)}, {e19, (3.38/10^4)}, {e46, (4.84/10^4)}, {e45, (7.89/10^6)}, {e36, (1.35/10^4)}, {e22, (3.38/10^4)}, {e64, (1/10^7)}, {e65, (1/10^7)}, {e70, (2.5/10^5)}, {e71, (2/10^3)}, {e39, (1.64/10^2)}, {e13, (2/10^3)}, {e62, (1/10^4)}, {e34, (1.35/10^4)}, {e31, (1.35/10^4)}, {e24, (3.38/10^4)}, {e60, (1/10^4)}, {e50, (5.66/10^4)}, {e49, (4.84/10^4)}, {e48, (7.89/10^6)}, {e37, (1.35/10^4)}, {e23, (3.38/10^4)}, {e42, (4/10^3)}, {e40, (4/10^3)}, {e41, (4/10^3)}, {e43, (4/10^3)}, {e67, (2/10^4)}, {e47, (5.66/10^4)}, {e69, (1.64/10^2)}, {e68, (2/10^3)}, {e59, (1/10^4)}, {e32, (1.35/10^4)}, {e63, (1/10^4)}, {e35, (1.35/10^4)}, {e21, (1.52/10^6)}, {e61, (1/10^4)}, {e33, (1.35/10^4)}, {e75, (1.52/10^6)}, {e30, (2/10^7)}, {e51, (5/10^7)}, {e52, (2/10^5)}, {e73, (1.52/10^6)}, {e78, (2/10^7)}, {e25, (1.58/10^4)}, {e17, (1.58/10^4)}, {e38, (1.1/10^2)}}];Subscript[ℱ, EDG] = FailureDistribution[bexprEDG, distsEDG];Grid@Map[Plot[Evaluate[#[Subscript[ℱ, EDG], t]], {t, 0, 30}, PlotRange -> {0, Automatic}, Filling -> Axis, PlotLabel -> #]&, {{SurvivalFunction, CDF}, {PDF, HazardFunction}}, {2}]