Question

the answer is 0.173... but how do I get it?

The local telephone company has a standby generator with a failure rate of 0.001 failures/hour to provide electrical power in case of a service interruption. History has shown that the electrical service has a failure rate of 0.00023 per hour. Assuming perfect switching, what is electrical power reliability for a year? a. 0.133 0.0.173 c. 0.203 d. 0.453

Answer 1

P(failure of generator) =1-e^{-0.001*365*24} =0.999843

P(failure of electric system) =1-e^{-0.00023*365*24} =0.866653

electric power reliability of the year =1-P(both electric service and standby generator fails) =1-0.999843*0.866653

=0.133

option A is correct