January 6, 2012



Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks

1. (a) Explain the general characteristics of the binomial distribution?
(b) A product is claimed to be 90% free of defects. What is the expected value and standard deviation of the number of defects in a sample of 4? [8+8]

2. (a) A series system has 10 identical components. If the overall system reliability must be at least 0.99, what is the minimum reliability required of each component?
(b) Define minimal cut set. Explain the reliability analysis of complex systems using minimal cutest method. [8+8]

3. (a) Derive the expressions for the expected value and standard deviation of the exponential distribution.
(b) Consider the following reliability function, where t is in hours:
R(t) = 1/(0.001t+1)t  0
i. Find the reliability after 100 operating hours and after 1000 operating
ii. Derive the hazard rate function. Is it an increasing or a decreasing failure rate. [8+8]

4. The following STPM shows the transitional rates in per hour of a continuous Markov process.
P =2
0.90 0.05 0.05
0 0.95 0.05
0 0 1
(a) Construct state space diagram.
(b) Evaluate the MTTF given that the system starts in state 1. [8+8]

5. A pumping station has two identical pumps connected in parallel, each capable of supplying 3000 gallons/hr. The failure rate and repair rate of each is 0.5 f/hr and 4 r/hr respectively. Evaluate the frequency of encountering and duration of residing in each possible throughput state. [16]

6. A system consists of 12 units of 20 MW each having a forced outage rate of 0.01. Develop the capacity outage probability table and hence determine the cumulative probability of various capacity states.

7. (a) Explain how probability of failure and expected frequency of failure at a bus can be estimated for radial configuration of composite generation and transmissions system.
(b) Define and explain the various annualized Load Point Reliability Indices used for Bulk Power Systems Reliability analysis. [16]

8. Consider the radial distribution system with circuit breaker, lateral distributor protection and disconnects  The failure rates and repair times of various components are given below.
Component ? (f/yr) r (hrs)
1 0.20 4
2 0.10 4
3 0.10 4
a 0.30 5
b 0.20 5
c 0.20 5
Evaluate the basic reliability indices of the system if fuse gear operates with a probability of 0.8.



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