In the circuit shown, the probability of any switch being closed is 0.8 and all events are independent. (a) What is the probability that a circuit will exist? (b) Given that a circuit exists, what is the probability that switches a and b are closed? Let the events that a, b, e and d are closed be A, B, C and D. Let X denote the event that the circuit exists. Serie se parallel

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1. In the circuit shown, the probability of any switch being closed is 0.8 and all events are independent.
(a) What is the probability that a circuit will exist? (b) Given that a circuit exists, what is the
probability that switches a and b are closed? Let the events that a, b, c and d are closed be A, B, C
and D. Let X denote the event that the circuit exists.
b.
Seriese
parallel
d
2. A system has 12 components. Components 1 through 8 are different have reliabilities 0.98, 0.99, 0.992,
0.975, 0.984, 0.978, 0.96, 0.995 respectively. Components 9 through 12 are the same, with reliability of
0.95. Components 4 through 6 are critical, and cach must operate for the system to function. However,
only one of the components 1 through 3 has to be working and the same for 7 and 8. At least two of
the four identical components must work, as well. Draw the system diagram and find the probability
that system survives.
3. A circular bar of 25 mm diameter is made of carbon steel and is subjected to axial force F. The mean
yield strength of the material is 250MPA and mean value of force F is 70kN. Both yield strength and
force are random variables and follow a normal distribution. The coefficient of variation of both variables
is 10%. Calculate the reliability index.
Transcribed Image Text:1. In the circuit shown, the probability of any switch being closed is 0.8 and all events are independent. (a) What is the probability that a circuit will exist? (b) Given that a circuit exists, what is the probability that switches a and b are closed? Let the events that a, b, c and d are closed be A, B, C and D. Let X denote the event that the circuit exists. b. Seriese parallel d 2. A system has 12 components. Components 1 through 8 are different have reliabilities 0.98, 0.99, 0.992, 0.975, 0.984, 0.978, 0.96, 0.995 respectively. Components 9 through 12 are the same, with reliability of 0.95. Components 4 through 6 are critical, and cach must operate for the system to function. However, only one of the components 1 through 3 has to be working and the same for 7 and 8. At least two of the four identical components must work, as well. Draw the system diagram and find the probability that system survives. 3. A circular bar of 25 mm diameter is made of carbon steel and is subjected to axial force F. The mean yield strength of the material is 250MPA and mean value of force F is 70kN. Both yield strength and force are random variables and follow a normal distribution. The coefficient of variation of both variables is 10%. Calculate the reliability index.
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