Solution Found!
A system contains two components, C and D, connected in
Chapter 2, Problem 37E(choose chapter or problem)
A system contains two components, C and D, connected in parallel as shown in the diagram.
Assume C and D function independently. For the system
to function, either C or D must function.
a. If the probability that C fails is 0.08 and the probability that D fails is 0.12, find the probability that the system functions.
b. If both C and D have probability of failing, what must the value of
be so that the probability that the system functions is 0.99?
c. If three components are connected in parallel, function independently, and each has probability of failing, what must the value of
be so that the probability that the system functions is 0.99?
d. If components function independently, and each component has probability 0.5 of failing, what is the minimum number of components that must be connected in parallel so that the probability that the system functions is at least 0.99?
Questions & Answers
QUESTION:
A system contains two components, C and D, connected in parallel as shown in the diagram.
Assume C and D function independently. For the system
to function, either C or D must function.
a. If the probability that C fails is 0.08 and the probability that D fails is 0.12, find the probability that the system functions.
b. If both C and D have probability of failing, what must the value of
be so that the probability that the system functions is 0.99?
c. If three components are connected in parallel, function independently, and each has probability of failing, what must the value of
be so that the probability that the system functions is 0.99?
d. If components function independently, and each component has probability 0.5 of failing, what is the minimum number of components that must be connected in parallel so that the probability that the system functions is at least 0.99?
ANSWER:
Answer
Step 1 of 4
a) Here C and D are 2 conductors connected parallely and function independently
P(C fails)=P(C’)
=0.08
P(C function)=P(C)
=1-0.08
=0.92
P(D fails)=P(D’)
=0.12
P(D function)=P(D)
=1-0.12
=0.88
P(That the system function)=P(CUD)
=P(C)+P(D)-P(C)P(D)
=0.92+0.88-0.92(0.88)
=0.9904