# Pune University Exam Paper

## RELIABILITY(2008 Course)

Instructions:

1        Answers to the two sections should be written in separate answer-books

2        Black figures to the right indicate full marks.

3        Neat diagrams must be drawn wherever necessary.

4        Use of electronic pocket calculator is allowed.

5        Assume suitable data, if necessary.

SECTION -I

Q.1 A Distinguish between Reliability and Quality of the product.        4

B   What is the relationship between MTTF and Reliability?         4

C   In the life testing of 10 elements of a mixture ,the time to failure for each element 8

is as below. Calculate the mean failure rate for 905 hours and the mean time to

failure for all the elements.

 Element Number Time to failure in hours 1 800 2 805 3 810 4 815 5 820 6 827 7 838 8 848 9 875 10 905

OR

 Q.2 A Describe the various components of the reliability-cost curve of the product. 6 B Explain the term Probability Density Function and Cumulative Distribution Function 4 C Explain failure density function, Hazard rate and Mean Time Between Failure. 6 Q. 3 A State various probability distributions. Explain any three of them. 6 B Explain Tie Set and Cut Set method of reliability evaluation. 6 C Find the reliability of system shown in fig, having S1 ,S2, S3 and S4 non series parallel structure. 6

OR

 6 6

Q. 4 A For a mechanical component following weibull distribution with = 2.5,^ = 3000 and I =1600.Find the reliability of the component and failure rate for the operating time of 2500 hrs.

 6

B Five elements (a,b,c,d and f) of a system are connected as shown in fig. which also indicate the reliability of each component.Find the system reliability.

 C Explain the active ,passive and stand by redundancies.

Q. 5          A     Describe dynamic programming apportionment technique.                                                       6

B      A system of three elements 1,2 and 3 having failure rates X 1=0.007, X 2=0.003,                  6

X 3=0.001 per hour respectively. Assuming mission time of 20 hours and system reliability of 0.90,find failure rates as well as reliability of each sub system for the entire mission period.

C      A system operating from the time t=0 Prove that the probability of the system                     4

functioning properly between time t 2 and t1 (since t 2 > t 1) is Rt 2 – t 1=1 – R(t 1) + R(t 2)

OR

Q. 6          A     Four units are connected in series with reliabilities R 1 = 0.83 , R 2 =0.89 , R3                       6

=0.79 AND R 4 =0.97.Calculate the system reliability. If the reliability is to be increased to a value of 0.65, how should this be apportioned among the four units according to minimum effort method?

B      Explain equal Apportionment and ARINC technique to determine the reliability.                6

C      What is reliability allocation? Write the advantages of reliability allocation                         4

method.

SECTION II

Q. 7           A      Explain reliability , maintainability and availability. What are the types of                          8

availabilities?

B       What is Maintainability function? From the basic maintainability equation show               8

that MTTR is the reciprocal of repair rate.

OR

Q. 8           A      For a computer unit a suitable air conditioning system has to be designed. It                        8

should have reliability valve of 0.95 for an operation of 800 hrs. The availability valve over the same period of time is required to be 0.98 .Assume constant hazards for failure and repair. Estimate MTBF and MTTR.

B       Distinguish between Breakdown Maintenance and Preventive Maintenance.                       4

 Q. 9 A               Explain the methodology of constructing Fault tree diagram. What are the various symbols used while constructing the fault tree diagram? B For the system shown in fig below, calculate the reliability using tie-set and cut­set theory.

 OR Q. 10 A The figure shows a fault tree diagram.The failure rate of each element is given as 8 X (a)=0.025, X (b)0.01 and X (c)=0.005 .Find out the failure rate of the system.

 8 8

C       Explain Reliability Centred Maintenance.                                                                                    4

Describe the method of obtaining critically of a component or a sub system using 8 Risk Priority Number (RPN).

 B Q. 11 A B

Explain the Markov model. How it is applied in reliability analysis of a system                                                         8

having constant hazard rate.

The following data refers to a certain test of equipment      10

 Failure No. 1 2 3 4 5 6 7 8 Operating time to failure(hrs) 18 12 08 22 26 35 30 40

Find out the reliability by

(i)               Mean Method and

(ii)             Median Method and compare the two by plotting.

OR

 Q. 12 A B c

Explain significance of “Safety margin “in engineering reliability design.                            6

Explain Accelerated life Testing for evaluation of reliability.                                                  6

The mean strength and standard deviation of a bolted joint are 3000 kgf/cm                        6

and 300 kgf/cm respectively. The joint is loaded such that stress induced has a mean valve of 2500 kgf/cm with standard deviation of 50 kgf/cm .Assuming that shear strength and the induced stresses are independent and normally distributed, find out the probability of survival of bolted joint. Statistical data is given below:____

 z 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0(Z) 0.8849 0.9032 0.9192 0.9331 0.9452 0.955 0.964