監視カメラの信頼性
カメラが重なり合う格子に配置されている．すべての領域は，2×2の格子が失敗するまでカバーされる．それぞれのカメラは，6年間の期待寿命を持つ．この系の信頼性と4つのカメラだけの系ムの信頼性を，待機成分がある場合とない場合で比べる．
structure = BooleanConsecutiveFunction[{2, 2}, {4, 4}][Array[Subscript[x, #1, #2]&, {4, 4}]];
𝒟camera = ExponentialDistribution[1 / 6];
ℱ = FailureDistribution[structure, Join@@Array[{Subscript[x, #1, #2], 𝒟camera}&, {4, 4}]];
ℱnooverlap = FailureDistribution[Subscript[x, 1] || Subscript[x, 2] || Subscript[x, 3] || Subscript[x, 4], {{Subscript[x, 1], 𝒟camera}, {Subscript[x, 2], 𝒟camera}, {Subscript[x, 3], 𝒟camera}, {Subscript[x, 4], 𝒟camera}}];
𝒟standby = StandbyDistribution[𝒟camera, {𝒟camera, 𝒟camera, 𝒟camera}, 0.9];
ℱstandby = FailureDistribution[Subscript[x, 1] || Subscript[x, 2] || Subscript[x, 3] || Subscript[x, 4], {{Subscript[x, 1], 𝒟standby}, {Subscript[x, 2], 𝒟standby}, {Subscript[x, 3], 𝒟standby}, {Subscript[x, 4], 𝒟standby}}];Plot[Evaluate@{SurvivalFunction[ℱ, t], SurvivalFunction[ℱnooverlap, t], SurvivalFunction[ℱstandby, t]}, {t, 0, 15}, Filling -> Axis, PlotLegends -> Placed[{"連続的", "重なりなし", "待機"}, Below]]