An automotive manufacturer recommends servicing brake systems and replacing worn

Question

An automotive manufacturer recommends servicing brake systems and replacing worn parts every 20,000 miles. A four-wheel vehicle has four brakes (two front brakes and two rear brakes). The reliability of a single brake has been found through reliability tests to be 0.8855 at 20,000 miles.

(a) If at least one front brake and one rear brake must function for a 4-wheel vehicle to safely stop, find the system reliability at 20,000 miles.

(b) What is the system reliability at 20,000 miles if at least any two brakes must function?

Explanation / Answer

a)probability that at least one  front brake function =1-P( none of front break functions) =1-(1-0.8855)2 =0.9869

similarly at least one of  rear brake works =0.9869

hence  system reliability =0.9869*0.9869 =0.9740

b) (Here I am assuming  at least any two brakes must function ,mean one of any 4 break works, please clarify)

system reliability =1-P( none of two breaks functions) =1-(0.9869)2 =0.9998

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