1. The logical expression for a fault tree is given by:

Find the minimum cut sets.

**A. **

B.

C.

D. None of these

2. Two pumps operating in parallel supply secondary cooling water to a condenser. The cooling demand

fluctuates, and it is known that each pump is capable of supplying the cooling requirements 80% of the time

in case the other fails. The failure probability for each pump is 0.12; the probability of both failing is 0.02. If there is a pump malfunction, what is the probability that the cooling demand can still be met?

A. 0.8

B. 0.12

C. 0.88

**D.0.08**

Let A= success of A, B=success of B, then,

3. Consider the discrete random variable defined by:

A. μ=23/36, σ2=1.31

**B. μ=55/36, σ2=55/36**

C. μ=55/36, σ2=1.9715

D. μ=55/36, σ2=1.404

4. If the CDF for times to failure is Find the failure rate as a function of time.

**A. 2/(t+10)**

B. 0.002

C. (t+10)/.2

D.(t+10)2 /2

5. A device has a constant failure rate of 0.7/year. What is the probability that the device will fail during the second year of operation?

A. .45

B. 0.2502

**C.0.503**

D. 0.602

6. There is a contractual requirement to demonstrate with 90% confidence that a vehicle can achieve a 100-km mission with a reliability of 99%. The acceptance test is performed by running 10 vehicles over a 50,000- km test track. What is the contractual MTTF?

A. 5000 km

**B. 9950 km**

C. 8525 km

D. 1950

7. The one-month reliability on an indicator lamp is 0.95 with the failure rate specified as constant. What is the probability that more than two spare bulbs will be needed during the first year of operation? (Ignore replacement time.)

A. 0.1026

**B. 0.0246**

C. 0.6155

D. 0.127

R=e-λt→0.95=e-λt; λ=0.0513 per month

λT=0.0513×12=0.6155 per year

8. A part for a marine engine with a constant failure rate has an MTTF of two months. If two spare parts are carried, What is the probability of surviving a six-month without losing the use of the engine as a result of part exhaustion?

A. 0.1026

**B. 0.0246**

C. 0.6155

D. 0.127

9. An engineer designs a system consisting of two subsystems in series. The reliabilities are R1 = 0.98 and R2 = 0.94. The cost of the two subsystems is about equal. The engineer decides to add two redundant components. Which of the following would it be better to do?

10. Find the variance in the time to failure, assuming a constant failure rate λ, for two units in active parallel.

A. 2/3λ

B. 3/2λ

C. 3/4λ2

**D. 5/4 λ2**