Car System Reliability

A car has four tires that are all needed to drive. Given the lifetime distribution of a tire as

ExponentialDistribution

, calculate the failure rate and mean time to failure (MTTF) of the car with respect to the tires

Define the distribution of each tire:

In[1]:=

=ExponentialDistribution[0.0004];

All tires should work simultaneously for the car to run:

In[2]:=

ℛcar=ReliabilityDistribution[x∧y∧z∧v,{{x,},{y,},{z,},{v,}}];

Compute the car system’s hazard rate (the probability the car fails in the next instant, given it has survived up to time 𝑡):

In[3]:=

HazardFunction[ℛcar,t]

Out[3]=



0.0016	t≥0
0	True

Mean time to failure (MTTF) of a car:

In[4]:=

Mean[ℛcar]

Out[4]=

625.

Simulate the lifetime of the car:

In[5]:=

Histogram[RandomVariate[ℛcar,1000],20,"Probability",ChartStyle"Pastel",FrameTrue,AxesFalse,FrameLabel{"Lifetime","Probability"},PlotLabel"Histogram of Car Lifetimes"]

Out[5]=

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