Question

4. The following circuit operates only if there is a path of functional devices from left to right. The probability that each device functions is shown on the graph. Assume that devices fail indepen- dently. What is the probability that the circuit operates? 0.9 0.9 0.9 0.9 0.95 0.99 0.95

Answer 1

here parallel block of 3 elements works =1-P(none of 3 works)=1-(1-0.9)*(1-0.95)*(1-0.95)=0.99975

probability that lower parallel branch works =0.99975*0.99=0.989753

probability that upper parallel branch works =0.9*0.9*0.9=0.729

hence P(circuit operates)=1-P(none of parallel branch works)

=1-(1-0.989753)*(1-0.729)=0.997223