WOLFRAM

Wolfram Language & System Documentation Center

Reliability of a Car

A car needs wheels, an engine, a transmission, and one out of two brake systems to function.

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]]}}];
Compute the survival function:
Wolfram Language code: SurvivalFunction[ℛcar, t]
Without maintenance, the expected lifetime is about three years:
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]
Simulate the lifetime of the car:
Wolfram Language code: ListPlot[{RandomVariate[ℛcar /. vals, 100], {{0, mttf}, {100, mttf}}}, Joined -> {False, True}, Filling -> Axis, AxesOrigin -> {0, 0}]