# Safety and Reliability Engineering Past Paper

**Topics:**Normal distribution, Probability theory, Probability density function

**Pages:**12 (1485 words)

**Published:**February 13, 2013

UNIVERSITY OF ABERDEEN

SESSION 2011 – 2012

Degree Examination in EG40JQ SAFETY AND RELIABILITY ENGINEERING Friday 20 January 2012

Notes: (i)

(ii)

2.00 p.m. – 5.00 p.m.

Candidates ARE permitted to use an approved calculator

Data sheets are attached to the paper.

Candidates should attempt all FIVE questions.

REGULATIONS:

(i)

You must not have in your possession any material other than that expressly permitted in the rules appropriate to this examination. Where this is permitted, such material must not be amended, annotated or modified in any way.

(ii)

You must not have in your possession any material that could be determined as giving you an advantage in the examination.

(iii)

You must not attempt to communicate with another candidate during the exam, either orally or by passing written material, or by showing material to another candidate, nor must you attempt to view another candidate’s work.

Failure to comply with the above will be regarded as cheating and will lead to disciplinary action as indicated in the Academic Quality Handbook (www.abdn.ac.uk/registry/quality/appendix7x1.pdf) Section 4.14 and 5.

You may not start reading the questions or writing until instructed to do so by the Invigilator.

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EG40JQ/12

Question 1:

a)

How do you define Risk? Explain the different risk assessment methods highlighting the relevant tools for each of these methods.

[8 marks]

b) The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.005 cm and a standard deviation of 0.001 cm.

i) What is the probability that the diameter of a dot exceeds 0.0065 cm? [2 marks]

ii) What is the probability that a diameter is between 0.0035 and 0.0065 cm? [2 marks]

iii) What standard deviation of diameters is needed so that the probability in part ( ii) is 0.995? [3 marks]

c) A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is normally distributed with a mean of 2 mm and a standard deviation of 0.1 mm and the halves are independent. Determine the reliability index corresponding to the probability that the total thickness exceeds 4.3 mm.

[5 marks]

Question 2:

a)

The natural frequency of a particular heavily-damped one degree of freedom mechanical system is given by

f

1

2

q 2500

m m2

where m is the mass and q is the stiffness. Write down the limit state corresponding to the event that f is less than 10 Hz. Calculate the corresponding probability of failure by performing Monte Carlo simulations with the following independent uniform random numbers.

Independent uniform random numbers

for m:

0.6324 0.9572 0.6557 0.6555 0.6948 0.1869

0.6551 0.7513

for q:

0.9058 0.9649 0.9157 0.7577 0.0462 0.3816

0.7547 0.3404

Assume that m and q are statistically independent and follow Normal distribution with the following parameters.

Qu. 2 continued overleaf/

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EG40JQ/12

Qu. 2 continued /

Basic variable

m

q

Mean

Standard deviation

60 kg

0.3 kg

3000 N/m 750 N/m

[13 marks]

b) In a study on the effect of ambient temperature (X) on the electric power consumed by a chemical plant (Y), following data were collected:

Y (BTU)

X (0F)

285

45

320

72

265

31

298

60

267

34

i) Evaluate the sample mean of X and Y.

[2 marks]

ii) Calculate the sample correlation coefficient between X and Y. Provide an interpretation of this quantity.

[5 marks]

Question 3:

a)

What do you understand by the concept of partial safety factor?

[3 marks]

b) The burst pressure in the case of intact pipes is given by 1.1 y (2t )

Pb

D

where y is the yield stress of the pipe material and D and t are respectively the outer diameter and wall thickness of the pipe. Using the following data, compute the reliability index corresponding to the probability of the burst pressure ( Pb) being less than an internal operating pressure of 6 MPa and...

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