Reliability of a vehicle can be expressed as the probability of the vehicle failure at a certain time. Suppose you are planning for a trip to Houston this weekend and you worry about the reliability of your car. In considering this, you figured out that failure of your car can be caused by engine failure, transmission failure and chassis failure, while engine failure can be caused by electronic system failure. This is represented by the following diagram:

Assume F=Car Failure, E=Engine failure, T=Transmission Failure, C=Chassis Failure, ES=Electronic Failure,

Use law of total probability to present the probability of car failure: Pr(F).

 

Mechanical Electronic Failure system Failure Chassis Engine Failure Transmission Failure Failure Car Failure