WOLFRAM

Wolfram Language & System Documentation Center

Airplane Safety

In order to fly, an airplane needs both wings, one engine out of two on each wing, and the air control system operating.

Wolfram Language code: {𝒟Motor, 𝒟Fuel, 𝒟Cooling, 𝒟Propeller} = {WeibullDistribution[1.58, 4830], WeibullDistribution[1.44, 5130], WeibullDistribution[1.60, 4190], WeibullDistribution[1.63, 3740]};
Wolfram Language code: ℛSingleEngine = ReliabilityDistribution[motor∧fuel∧cooling∧propeller, {{motor, 𝒟Motor}, {fuel, 𝒟Fuel}, {cooling, 𝒟Cooling}, {propeller, 𝒟Propeller}}];
Wolfram Language code: ℛEngines = ReliabilityDistribution[(engine1∨engine2)∧(engine3∨engine4), {{engine1, ℛSingleEngine}, {engine2, ℛSingleEngine}, {engine3, ℛSingleEngine}, {engine4, ℛSingleEngine}}];
Wolfram Language code: parameters = {{1.85, 1.57, 2.25, 0.95, 0.73, 1.14, 0.92, 1.65}, {4729.02, 4718.22, 5843.58, 3956, 2672.1, 3977.39, 2895.62, 3994.78}};
Wolfram Language code: {𝒟Directional, 𝒟Longitudinal, 𝒟Lateral, 𝒟Flaps, 𝒟Trim, 𝒟Hydraulic, 𝒟LandingGear, 𝒟Steering} = Flatten[Transpose[{MapThread[WeibullDistribution, parameters]}]];
Wolfram Language code: ℛACS = ReliabilityDistribution[x1∧x2∧x3∧x4∧x5∧x6∧x7∧x8, {{x1, 𝒟Directional}, {x2, 𝒟Longitudinal}, {x3, 𝒟Lateral}, {x4, 𝒟Flaps}, {x5, 𝒟Trim}, {x6, 𝒟Hydraulic}, {x7, 𝒟LandingGear}, {x8, 𝒟Steering}}];
Wolfram Language code: 𝒟Wing = WeibullDistribution[1.79, 4250];
Wolfram Language code: ℛAirplane = ReliabilityDistribution[enginesystem∧wing1∧wing2∧acs, {{enginesystem, ℛEngines}, {wing1, 𝒟Wing}, {wing2, 𝒟Wing}, {acs, ℛACS}}];
The Fussell–Vesely importance for the different parts of the engine:
Wolfram Language code: Plot[Evaluate@FussellVeselyImportance[ℛSingleEngine, t], {t, 0, 1000}, Filling -> Axis, PlotLegends -> {"Motor", "Fuel", "Cooling", "Propeller"}, ImageSize -> Medium]