52205-mt----reliability Engineering

NR

Code No: 52205/MT

M.Tech. – II Semester Regular Examinations, September, 2008 RELIABILITY ENGINEERING (Common to Power Electronics & Electric Drives/ Power & Industrial Drives/ Power Electronics/ Electrical Power Engineering) Time: 3hours

Max. Marks:60

Answer any FIVE questions All questions carry equal marks --1. a) What are the necessary conditions to be satisfied by a random variable. b) Mention the important properties of a random variable. c) Suppose that the life time of a certain kind of an emergency backup battery (in hours) is a random variable X having a Weibull distribution α = 0.1, β = 0.5. Find i) Mean time of these batteries, ii) The probability that such a battery will last more than 300 hours, iii) The probability that such a battery will not last 100 hours. 2. a) Define hazard rate. What is the difference between hazard rate and constant failure rate? b) For R(t) = i) ii) iii) iv)

e

0.001t

t≥0

Computer the reliability for a 50 – hr mission. Show that hazard rate is decreasing. Given a 10-hr burn – in period, compute the reliability for a 50 – hr mission. What is the design life for a reliability of 0.95 given a 10 – hr burn – in ?

3. a) Explain the significance of Bath – Tub curve and with a suitable example explain how will you proceed to construct the curve. b) A system is composed of three components. Component 1 is in series with the parallel combination of components 2 and 3. Given λ1 = 2 failures per year and λ2 = λ3 = 3 failure per year. Calculate the reliability and MTTF of the system for a mission time of 1000 hours. Contd…2

Code No: 52205/MT

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4. a) Explain the reliability evaluation of series and parallel configurations. b) In the reliability logic diagrams shown in figure 1. out of components 4,5,6 at least two of the three must function for system success. Evaluate the expression for reliability of the system if each component has a probability of failure of 0.2.

Figure-1 5. a) Explain what is meant by ‘Minimal Cut – set’ in connection with reliability evaluation of a system. b) The reliability network of a system is given below. Figure.2 The figures on components indicate their reliabilities. Calculate the reliability of the system using the method of cut – sets.

Figure2. 6. a) Sketch the state transition diagram for Markov chains for the following state transition probability matrix. 0  0.5 0.5 0 1 0 0 0   P= 0.5 0 0.2 0.2     0 0.2 0.2 0.5

Contd …3 Code No: 52205/MT

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b) For the system shown in Figure 3. below, obtain the time domain expression and the steady state values of probabilities P1(t) and P2(t)

Figure3. 7. A certain part of machine can be in two states: working or undergone repair. A working part fails during the course of the day with probability (a). A part undergoing repair is put into working order during the course of a day with probability (b). Let Xn be the state of the part. i) Show that Xn is a two state Markov chain and give its one – step transition probability matrix P. ii) Find the n – step transition probability matrix Pn. iii) Find the steady state probability for each of the two states. 8. a) A network made up of four independents representing a system is shown in figure 4. Each block in the figure denotes a unit. The reliability of R of each unit is given. Calculate the network reliability by using the network reduction method.

Figure 4. b) What is the main disadvantage of the delta – star method used for network reduction? ^^^