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车的可靠性

一辆车需要有轮子、引擎、传动装置和两个刹车系统中的一个才能正常工作.

Wolfram Language code: ℛcar = ReliabilityDistribution[wheels∧engine∧transmission∧(brake1∨brake2), {{wheels, ExponentialDistribution[Subscript[λ, 1]]}, {engine, WeibullDistribution[a1, b1]}, {transmission, ExponentialDistribution[Subscript[λ, 2]]}, {brake1, ExponentialDistribution[Subscript[λ, 3]]}, {brake2, ExponentialDistribution[Subscript[λ, 3]]}}];
计算生存函数：
Wolfram Language code: SurvivalFunction[ℛcar, t]
不保养的话，期望寿命大约是3年：
Wolfram Language code: vals = {Subscript[λ, 1] -> (1/5), Subscript[λ, 2] -> (1/10), Subscript[λ, 3] -> (1/15), a1 -> 5, b1 -> 12};
Wolfram Language code: mttf = NExpectation[t, tℛcar /. vals]
模拟车的寿命：
Wolfram Language code: ListPlot[{RandomVariate[ℛcar /. vals, 100], {{0, mttf}, {100, mttf}}}, Joined -> {False, True}, Filling -> Axis, AxesOrigin -> {0, 0}]