A car with broken high-beam headlights is strained in a deserted area within the

Question

A car with broken high-beam headlights is strained in a deserted area within the Arctic Circle during a winter period without any sun light or even any moon light. The only way for the driver to drive this car out of the Arctic Circle is by using the two low -beam head lights of the car Suppose that, for the intended trip from the strained position to the edge of the Arctic Circle region, the reliability of each low-beam head light is 0.85 under the cold conditions Determine the reliability for this car in the context of the driver driving the car out of the Arctic Circle.

Explanation / Answer

solution:

1)reliabilty is nothing but probability that given system will work properly for given period of time under operating conditions of system.

2)here as car is strained in far arctic circle area,where no availability of natural light and high beam headlight is broken so only option is to use low beam headlight.

3)for proper working of system any one low beam headlight has to stay in operation till end of trip,so this system will be modelled as

input=(headlight 1 or headlight2)=output

reliability of low beam headlight is

R1=.85

R2=.85

so overall system realiability is given by if two headlight connected in parallel across output

Rsystem=[1-(1-R1)(1-R2)]

Rsystem=[1-(1-.85)(1-.85)]=0.9775

hence reliability of car to make safe trip out of arctic circle is Rsystem=.9775 or 97.75%

Rsystem=0.9775.

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