ramin_shamshiri_risk_analysis_exam2.pdf

7/30/2019 Ramin_Shamshiri_Risk_Analysis_Exam2.pdf

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Ramin Shamshiri EMM5622, EXAM II

EMM5622, RISK ANALYSIS IN ENGINEERING

EXAM II

Ramin Shamshiri


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Question 1

A project schedule network has two paths of tasks needed to compute the total time to complete the project.

They are either or as shown by the following time functions

Compute the probability of ( ) by calculating the reliability index () using

a. First-order reliability methodb. Advanced second-moment method

The noncorrelated random variables are assumed to have the following probabilistic characteristics:

Random Variable Mean Value Coefficient of Variation Distribution Type

1 0.25 Normal

5 0. 50 Normal 4 0.05 Normal 3 0.20 Normal 10 0.25 NormalSolution a:

() () () () () Coefficient of Variation:

Also ;


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It can be seen than

Random Variable MeanValue

Coefficient of Variation Standard Deviation 1 0.25 0.25 5 0. 50 2.5 4 0.05 0.2 3 0.20 0.6 10 0.25 2.5


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Solution b:

()

Solving yields Solving yields

Random

Variable

Mean

Value

Coefficient of

Variation

Standard

Deviation

Directional Cosines

for T1Directional Cosines

for T2

1 0.25 0.25 0.09919

5 0. 50 2.5 0.697139 4 0.05 0.2 0.079352 3 0.20 0.6 0.167313 10 0.25 2.5 0.9919 0.697139 () ()

(

)

() () () 5.951394

()

(

)

() () () () 5.019404

It can be seen than


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Question 2

Describe four engineering systems that can be modeled using the black-box method. What are the inputs

and outputs for each system?

Solution:

A schematic of the black-box system model is shown in the above figure. A structural engineer mightobserve the deflection of a bridge as an output of a input such as load at the middle of its span. By varyingthe intensity of the load, the deflection chances, hence by producing a relationship such as y=f(x) where x isan input variable, y is an input variable and f is a function that relates input to output.

Example 1: Probable maximum loadInput: Meteorological and Hydrological conditionsOutput: Flood runoffSystem: River Catchment Basin

Example 2: Greenhouse Environmental Control

Input: Heating and cooling loadSystem: Relevant actuators

Output: Environment temperature and relative humidity

Example 3: DC motor speed control

Input: Variable voltage to the systemOutput: Speed of the motor shaft in rpmSystem: DC motor

Example 4: VehicleInput: Amount of gas provided to the engine

Output: Speed or performance of the vehicleSystem: Engine and other components

SYSTEM

Input X Output Y


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Question 3

An engineer inspects a piece of equipment and estimates the probability of the equipment running at peak

efficiency to be 80%. She/he then receives a report that the operating temperature of the machine has

exceeded an 80C critical level. Past records of operating performance suggest that the probability of

exceeding the 80C temperature when the machine is working at peak efficiency is 0.4. Also, the probability

of the temperature being exceeded if the machine is not working at peak efficiency is 0.85.

a. Revise the engineers initial probability estimate based on this additional information from pastrecords

b. Draw a probability tree for this situationSolution a:

Event A: Exceeding 80CEvent B: Running at peak efficiency

=> => Posterior probability of variables B after variable () has occurred

Total=

Total=


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Solution b:


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Question 4

Using the data of example 4.21 as provided in Table 4.23 (from the textbook), and assuming five identical

components connected in series, compute , and function for a system in series. Thecomponent hazard function is given by the following equation:

Solution:

ramin_shamshiri_risk_analysis_exam2.pdf

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