# Pune University Exam Paper

## RELIABILITY(Elective-II)(Sem.- II)

Instructions to the candidates:

1)             Answer three questions from each Section.

2)             Attempt Q1 or Q2, Q3 or Q4, Q5 or Q6 from Section -1.

3)             Attempt Q7 or Q8, Q9 or Q10, Q11 or Q12 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) The following failure data is collected for a group of 100 accelerometers.

Find Failure density, hazard rate and reliability and also plot the results.[10]

 Timeinterval (hrs) 1 2 3 4 5 6 7 8 9 10 No. of failures 21 13 9 7 6 6 5 7 11 15

b)           Explain availability and maintainability of a system. The data is collected for a CNC machining center in a plant as follows : Calculate operational availability and inherent availability of the plant :                                                                                   [8]

Mean time before failure : 65 Hrs Mean time to repair : 10 Hrs Administrative logistic time : 125% of MTTR Calculate the operational availability and inherent availability of the CNC machining center in a plant.

OR

P.T.O.

Q2) a)       A machinist produced 100 shafts according to the specifications. During

inspection, the diameters of 85 shafts were found to be within the tolerance limits and 15 were found to be outside the tolerance band. If 6 shafts are randomly selected, find the probability of finding the diameter of at least one shaft falling outside the tolerance limits. [8]

b)         Find the reliability and MTBF of an engine for an operating time of

500 hrs if the rate is 4 per 106 hour.                                                                [5]

c)         For a system the mean time between failure is 90 hrs and down time of

system is 10 hrs. Find the system unavailability. For a mission time of 50 hrs what will be Reliability of the system.                                                                                  [5]

Q3) a)       Ten identical components are connected in parallel to achieve the system

reliability of 0.92. Determine the reliability of each component. How much additional number of components to be added in parallel to increase the reliability upto 0.98. [8]

b)         Explain the total probability theorem with suitable example. [4]

c)         State the distributions used in probability theory. Explain any one in

detail.                                                                                                                    [4]

OR

Q4) a)       Explain the central limit theorem & skewness coefficient.                           [6]

b)    Explain failure rate-time curve with its distinct regions of failure. Also

explain the causes of failure and unreliability.                                           [10]

Q5) a)       In a life test on the sample of 20 electric bulbs, they failed at thefollowing test hours.                                                                [8]

 840 1060 1225 1331 861 1100 1251 1348 901 1137 1270 1362 939 1184 1296 189 993 1200 1314 1401

Determine the MTTF of these bulbs and reliability at 1300 hrs. b) i) In a Parallel system if we need at least one out of 4 units to operate for the successful working of the system, determine the expression for reliability in terms of X and t. ii) If the failure rate X for above parallel system is considered as 0.005 and mission time 100 hrs find the reliability of the system. 8

OR

Q6) a)

 Fig. 1 shows a system configuration. The block shows elements of system and the reliability values of each element are given as R(A) = 0.96, R(B) = 0.94, R(C) = 0.99, R(D) = 0.85, R(E) = 0.90 & R(F) = 0.92. Find the system reliability.                                                                               [8]

 b)

Fing. 2 shows a reliability block diagram for the system. R(1) = 0.88, R(2) = 0.95, R(3) = 0.92, R(4) = 0.80, R(5) = 0.90, find the system reliability using conditional probability method.           [8]

SECTION – II

 Q7) a) b)

What are the different types of loads considered in designing any machines or structures? Explain those in brief.                                                                                                                 [8]

The mean strength and the standard deviation of a bolted joint are 3000 kg/cm2 and 250 kg/cm2 respectively. The joint is loaded such that stress induced has a mean value of 2500 kg/cm2 with a standard deviation of 50 kg/cm2. Assuming that shear strength and the induced stresses are independent and normally distributed, find out the probability of survival of the bolted joint. Extract of data from statistical table is given below :                                                                       [8]

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

 Q8) a)

Find the reliability and the corresponding central factor of safety of a system for which ps = 35000 kg/cm2 and pL = 30000 kg/cm2. Gs = 3000 kg/cm2 and ql = 1000 kg/cm2 and S 8 L follows normal distribution. The table shows normal variant (z) and ®(z).                         [8]

 Z 1.56 1.58 1.6 O(z) 0.9406 0.9429 0.9452

b) Derive an expression for reliability using load-strength interaction. [8]

Q9) a) Explain the fatigue failure and factors considered for fatigue design of mechanical components.                                                                                                        [8]

b) Explain the magnified loading and sudden death testing for a system.[8]

OR

Q10)a) Explain the procedure involved in FMECA. Also give the typical FMECA form.        [8]

b) In a short sample life testing of a system the following data is recorded. [8]

 Component 1 2 3 4 5 6 7 8 9 10 MTTF(Hrs) 10 12 15 24 28 30 35 38 40 45
 Plot the variation of reliability against time using i) Mean and ii) Median Ranking Method.

Q11)a) Explain various symbols used in construction of Fault tree diagram. [8] b) The fault tree diagram is shown in Fig. 3. The failure probabilities of the elements are as given below. E1 = E2 = 0.01, E3 = E4 = 0.002, E5 = E6 = 0.1. Find out the failure probability of top event and system reliability. [10]

 OR

Q12)a)

 Fig. 4 shows reliability block diagram of a system the reliabilities of each elements are given as R(A) = 0.92, R(B) = 0.90, R(C) = 0.98, R(D) = 0.86 & R(E) = 0.95. Find the system reliability. Also state tie sets and cut sets for the system.                                                                             [10]

b)

 Fig. 5 shows a reliability block diagram for a system. Construct a fault tree diagram for this system. If all the elements are having failure probability of 0.1, calculate system failure using fault tree analysis.[8]