## RELIABILITY ENGINEERING AND APPLICATION TO POWER JNTU previous years question papers

Time: 3 hours Max Marks: 80

All Questions carry equal marks

1. A die is thrown 6 times. Evaluate the probability of getting two spots on the upper face 0,1,2...,6 times and draw the probability density function and the probability distribution function. [16]

2. Consider the system in which success requires that at least one
of the paths, AC, BD, AED, BEC is good. Evaluate a general expression for system success and the reliability of the system if each component has a reliability of 0.95 using tie set method. [16]

3. (a) Show that the expected value and standard deviation of an exponential distribution are equal.
(b) The hazard rate of a device is ? (t) = 1pt . Deduce:
i. The probability density function
ii. The survivor function
iii. The expected value, and
iv. The variance. [8+8]

4. (a) Explain the two state Markov process of a single component with repair.
(b) Derive the expression for limiting state probabilities of a two component repairable model with identical capacities and identical transitional rates. [8+8]

5. Develop the state space model of four identical units having capacity of 50 MW each and unavailability of 0.04. Mark the various transitional rates of combined capacity state model if failure rate of each unit is 0.4 failures/ year and 9.6 repairs per year. Hence evaluate the cumulative probability and cumulative frequencies of various combined capacity states

6. (a) Explain how loss of load probability can be estimated using Load duration curve.
(b) The daily peak distribution of load is described by the relative frequency. Consider that there are three units of 20 MW each and one unit of 40 MW, each having a forced outage Rate of 0.04. Compute the loss of load probability of the system. [8+8]

7. (a) Describe with state space diagram, the Morkov model for a single transmission line under two weather environment.
(b) Two transmission lines A and B with ?N=2×10-4 f/day in normal weather and ?W=5×102 in severe weather and with repair rate, µ, of 1 r/day in both the weather supply a load. The mean duration of normal weather is 0.1 day. Calculate the probability of failure of supply to the load. [8+8]

8. Consider the radial distribution system  The failure rates and repair times of various components are as given below.
Component ? (f/yr) r (hrs)
1 0.20 5
2 0.10 5
3 0.10 5
4 0.30 5
5 0.30 5
6 0.20 5
7 0.20 5
8 0.10 5
The total isolation and switching time is 1 hour. Evaluate the basic load point reliability indices.

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