A circuit comprises 100 components. The circuit fails if one of the components f

Question

A circuit comprises 100 components. The circuit fails if one of the components fails, The time to failure of one component is exponentially distributed with a mean time to failure of 10 years. This distribution is the same for all components and the failure of each component is independent of the others. What is the probability that the circuit will be in operation for at least one year without interruption due to failure? What should the mean time to failure of a single component be so that the probability that the circuit will be in operation for at least one year without interruption is 90%?

Explanation / Answer

mean is 10 years

Probability that one component doesnt fail for 1 year =exp(-1/10)

Probability that 100 component doesnt fail for 1 year = (exp(-1/10))^100 =4.54*10^-5

b) (exp(-1/x))^100=0.9

=>x=-1/ln(0.9^(1/100)) =949.12 years

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