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Model with Reliability Block Diagrams

Model the reliability of systems with ReliabilityDistribution.

Wolfram Language code: series = [image]; parallel = [image]; mixed = [image];
Wolfram Language code: {Subscript[𝒟, 1], Subscript[𝒟, 2], Subscript[𝒟, 3]} = Table[ExponentialDistribution[1 / i], {i, 3}]; ℛseries = ReliabilityDistribution[Subscript[x, 1]∧Subscript[x, 2], {{Subscript[x, 1], Subscript[𝒟, 1]}, {Subscript[x, 2], Subscript[𝒟, 2]}}]; ℛparallel = ReliabilityDistribution[Subscript[x, 1]∨Subscript[x, 2], {{Subscript[x, 1], Subscript[𝒟, 1]}, {Subscript[x, 2], Subscript[𝒟, 2]}}]; ℛmixed = ReliabilityDistribution[Subscript[x, 1]∧(Subscript[x, 2]∨Subscript[x, 3]), {{Subscript[x, 1], Subscript[𝒟, 1]}, {Subscript[x, 2], Subscript[𝒟, 2]}, {Subscript[x, 3], Subscript[𝒟, 3]}}];
Wolfram Language code: sf[d_] := Plot[Evaluate[SurvivalFunction[d, t]], {t, 0, 3}, Filling -> Axis, Ticks -> {None, Automatic}]
Wolfram Language code: data = {{"Block Diagram / System", "SurvivalFunction[ℛ,t]"}, {Column[{series, "ℛ = ReliabilityDistribution[SubscriptBox[x, 1] ∧ SubscriptBox[x, 2],{{SubscriptBox[x, 1], SubscriptBox[𝒟, 1]}, {SubscriptBox[x, 2], SubscriptBox[𝒟, 2]}}]"}, Center], sf[ℛseries]}, {Column[{parallel, "ℛ = ReliabilityDistribution[SubscriptBox[x, 1] ∨ SubscriptBox[x, 2], {{SubscriptBox[x, 1], SubscriptBox[𝒟, 1]}, {SubscriptBox[x, 2], SubscriptBox[𝒟, 2]}}]"}, Center], sf[ℛparallel]}, {Column[{mixed, "ℛ = ReliabilityDistribution[SubscriptBox[x, 1] ∧ (SubscriptBox[x, 2] ∨ SubscriptBox[x, 3]), {{SubscriptBox[x, 1], SubscriptBox[𝒟, 1]}, {SubscriptBox[x, 2], SubscriptBox[𝒟, 2]}, {SubscriptBox[x, 3], SubscriptBox[𝒟, 3]}}]"}, Center], sf[ℛmixed]}};
Wolfram Language code: Grid[data, Frame -> All, FrameStyle -> Directive[White, Thick], Background -> {None, {Lighter[Blue, .9], {Hue[.6, .15, .9], GrayLevel[.9]}}}, BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 10}, ItemStyle -> {Automatic, {Directive[Bold, FontSize -> 12]}}, Spacings -> {1.5, 1.5}, ItemSize -> {Automatic, {2, Automatic}}]