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Reliability Engineering (Elective II) (April 2010)

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Total No. of Questions : 12] [Total No. of Pages : 7 [3764]-148 P1316 B.E. (Mechanical) RELIABILITY ENGINEERING (Elective - II) (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to candidates : 1) Answer three questions from each section. 2) Attempt Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6 from Section I. 3) Attempt Q.7 or Q.8, Q.9 or Q.10, Q.11 or Q.12 from Section II. 4) Neat diagrams must be drawn wherever necessary. 5) Assume suitable data, if necessary. 6) Figures to the right indicate full marks. 7) Use of non-programmable electronic calculators is allowed. SECTION - I Q1) a) In a survival test conducted on 100 cardboard boxes for their strength under impact loading, the following results were obtained. [10] No. of impacts 20 22 24 26 29 32 35 37 40 Number of boxes failed 7 10 15 14 15 13 13 8 5 Calculate failure density, hazard rate and reliability. b) The random variation w.r.t. time in the output voltage of systems are exponentially distributed with mean value of 100 V. What is the probability that the output voltage will be found at any time to lie in the range of 90-110V. [8] Q2) a) Explain availability and maintainability. Explain the types of availability in detail. [8] P.T.O. b) The following data refers to an availability study in a flexible manufacturing system using identical FMM. Find the inherent and operational availability. Assume administrative logistic time as 150% of MTTR. [10] No.of months Uptime (Hrs) Occurrence of failure MTTR (Hrs) Spares Management Time (Hrs) 1 380 3 0.75 0.8 2 355 2 0.85 1.2 3 330 2 2.5 3.55 4 345 1 4.5 1.75 5 335 2 3.5 2 6 366 2 1.5 3.5 Q3) a) Find the reliability of the system shown in Fig. 1. The reliability value of components 1, 2, 3, 4, 5 and 6 are 0.9, 0.85, 0.98, 0.87, 0.94 and 0.89 respectively. [8] b) The failure rates of three components are 0.05 f/yr, 0.01 f/yr and 0.02 f/yr respectively and their average repair times are 20 hrs, 15 hrs and 25 hrs resp. Evaluate the system failure rate, average repair time and unavailability if all three components must operate for system success.[8] [3764]-148 2 Q4) a) A manufacturing concern specializing in high pressure relief valve to a particular acceptance test before certifying it as fit to use. Over a period of time, it is observed that 95% of all valves manufactured pass the test. However the acceptance test adopted is found to be only 98% reliable. Consequently a valve certified as fit for use has a probability of 0.02 being faulty. What is the probability that the satisfactory valve will pass the test. b) [8] Explain the features of two parameter and three parameter weibull distribution. Q5) a) [8] Allocate failure rates and reliabilities for the following data if the reliability goal is 0.98. [8] i Importance factor Operating time 1 25 1 12 2 100 0.95 9 3 70 0.9 10 4 b) No.of modules 80 1 12 A system consists of ten components connected in series. The predicted reliabilities obtained from failure data are given in table. It is desired that the system reliability be 0.97. Determine reliability goal for all components. [8] Component No. Predicted reliability [3764]-148 1 2 3 4 5 6 7 8 9 10 0.95 0.98 0.96 0.99 0.97 0.99 0.98 0.98 0.97 0.98 3 Q6) a) Fig. 2 shows a system configuration. The block shows elements of system and each element has reliability. 0.95. Find the system reliability. [10] b) Define tie sets & cut sets. Write all possible tie sets and cut sets for the system shown in Fig. 3. Give minimal tie sets and minimal cut sets. [6] SECTION - II Q7) a) What are the types of loads considered in designing machines and structures? [8] b) Tests conducted on a sample of 100 automobile breaks have yielded a mean value of 56,669.5 and a std. deviation of 12,393.64 miles for the life of brakes. Assuming normal distribution find the probability of realizing the life of brakes less than 50,000 miles. Table shows (z) values. [8] Z 0.54 (z) [3764]-148 0.53 0.7019 0.7054 4 Q8) a) Fig. 4 Shows the fault tree diagram. The failure rates of each basic element is given. Find out the failure rate of the system. b) [8] Construct a fault tree for the system failure shown in Fig. 5. If all the elements are having failure probability of 0.1, calculate system failure using fault tree analysis. Q9) a) [8] Find the reliability and the corresponding central factor of safety of a system for which kg/cm2 and L s = 15000 kg/cm2 and L = 10000 kg/cm2. = 3000 = 1000 kg/cm2 and S & L follows normal distribution. The table shows normal variant (z) and (z). Z 1.56 1.58 1.60 (z) [3764]-148 s 0.9406 0.9429 0.9452 5 [8] b) Ten identical components are connected in parallel to achieve the system reliability of 0.9. Determine the additional number of components to be added in parallel to increase the reliability to 0.95. Q10)a) b) [8] Explain the procedure of Failure mode effects analysis. [8] In a short sample life testing of a system the following data are recorded. Component 1 2 3 4 5 6 7 8 MTTF (Hrs) 10 15 12 24 18 22 30 38 Plot the variation of reliability against time using: i) Mean and ii) Median Ranking Method. Q11)a) [8] Explain the magnified loading and sudden death testing for any system.[8] b) The fault tree diagram is shown in Fig. 6. The failure probabilities of the elements are as given below. E1 = E2 = 0.005, E3 = E4 = 0.02, E5 = E6 = 0.1. Find out the system reliability. Also draw reliability block diagram for the same. [3764]-148 [10] 6 Q12)a) Fig. 7 shows reliability block diagram of a system. The reliabilities of each elements are given as R(A) = 0.96, R(B) = 0.92, R(C) = 0.99, R(D) = 0.85 & R(E) = 0.90. Find the system reliability. Also state tie sets and cut sets for the system. b) [10] Determine the reliability of system using event tree diagram if four subsystems are connected in series and management considers the system giving satisfactory performance even if two out of four units remain out of order. The failure rate of each subsystem is 1 in 2000 and working hours are 400. [8] Y [3764]-148 7

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