Probabilistic Methods in Engineering
Engineering 9411
Final Examination
Vijayakumar Ramamoorthy
1. Aggregates for a highway pavement are extracted from a gravel pit. Based on experience with
the material from this area, it is known that the probabilities

Memorial University of Newfoundland
Faculty of Engineering and Applied Science
Engineering 9411
Probabilistic Methods in Engineering
Final Examination (Openbook sample)
3 hours
Attempt all questions. All questions have the same marks.
1.
The capital cost

Engineering 9411
Assignment 2
Vijayakumar ramamoorthy (201585072)
1) In considering the safety of a building, the total force acting on the columns of the
building must be examined. This would include the effects of the dead load D (due to the
weight of t

Assignment 4
Engineering 9411
Due date: Nov. 26th , 2015
1.
Assume that we know air pollution and smoking are two main
contributors to lung cancer. Dysponea is an indictor of impaired breath as
a symptom of lung cancer. X-ray can be used to support the di

Application of Probabilistic methods to predict individual
match results in the Indian Premier league (IPL):
Vijayakumar Ramamoorthy1, Saravana kumar Selvaraj2
1,2
Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St.Johns,

Memorial University of Newfoundland
Faculty of Engineering and Applied Science
Engineering 9411
Probabilistic Methods in Engineering
Take Home Final Examination
Dec. 14-15 (6 p.m.) 2016
Evaluation: 30%
Attempt all 4 questions. Marks are as shown. You may

Monte Carlo Simulation
The Monte Carlo method uses a pseudorandom number generator to generate numbers
uniformly between zero and one. A simple random number generator uses Lehmers
recursion, i.e.
zn = azn-1 mod m, zo=1
Normalizing zn, one obtains a unifo

_
Reliability Statistics (1)
failure rate
(t)
early
the reliability bathtub
curve
wear-out
useful
time
:
Exponential distribution:
Lognormal distribution:
f(t) = e
= cte = 1/MTTF
f(t) =1 /t(2)
10[ ] = t50%
MTTF = Mean Time To
Failure
= time for 63% failu

10-601 Machine Learning
Midterm Exam
Fall 2011
Tom Mitchell, Aarti Singh
Carnegie Mellon University
1. Personal information:
Name:
Andrew account:
E-mail address:
2. There should be 11 numbered pages in this exam.
3. This exam is open book, open notes.

SOLVING PROBABILITY PROBLEMS
USING COMPUTER SIMULATIONS
ON MINITAB
Leonard M. Lye, PhD, PEng, FCSCE
Professor of Civil Engineering
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
3rd Edition
Copyright 1995, 2000, 2002 by Leo

Assignment#2 : The Failure Distribution
Submission date: May 29, 2014
1.
Consider the following reliability function, where t is in hours:
R t
1
0.001t 1
t 0
(a) Find the reliability after 100 operation hours; after 1000 operating hours.
(b) Derive the h

Assignment 4: Reliability of systems
Due date: Thursday, July 10th, 2014
1. Find the minimum number of redundunt components, each having a reliability of 0.4,
necessary to achieve a system reliability of 0.95. There is also a common mode
failure probabili

Chapter 11: Exercise Questions
1.
A system has a lognormal repair distribution with a median time to repair of 3.5 hr
with s=0.18. Specifications call for 95% of the maintenance to be completed
within 5 hr and the number of maintenance hours to be less th

Memorial University
Faculty of Engineering & Applied Science
Reliability Engineering, ENGI 9116
Take Home Final Examination
Date: April 15-17, 2017
Please submit your final exam in Bruneau Centre (IIC 1008) or in drop box of ENGI 9116
on or before April 1

Chapter 12: Exercise Questions
1.
A component has MTBF = 200 hr and MTTR = 10 hr with both the failure and
repair distribution exponential, what is the availability at 10 hr, for first 10 hours
and at steady state?
2.
A fire alarm has a constant failure r

Chapter 10: Exercise Questions
1. A requirement exits for an engine fuel pump to be repaired (or replaced) within 3
hours 90% of time. If the repair distribution is lognormal with s =0.45, what
MTTR should be achieved to meet this goal?
2. A cutting tool

Assignment 3
Engineering 9411
Due date: Nov. 17rd, 2015
1. The occurrence of flaws in a weld joint may be modeled by a Poisson
process with a mean occurrence rate of flaws per meter of weld. Actual
observation with a powerful device (assume it would not m

Memorial University of Newfoundland
Faculty of Engineering and Applied Science
Engineering 9411
Probabilistic Methods in Engineering
Take Home Final Examination
3 days
Attempt all questions. Marks are as shown. All work must be your own and you
must not c

Fall 2014
M.Yang
ENGINEERING 9411
PROBABLISTIC METHODS IN ENGINEERING
Instructor:
TA:
Dr. Ming Yang
Office: IIC 1017, Email: [email protected]
Mr. Jalil Shadbahr
Office: EN 2055, Email: [email protected]
Introduction:
Uncertainties are unavoidable in the design

ENGI 9411
Fall 2014
P(Ac)=
1-P(A)
If AB, then
P(A)P(B)
P(AUB)=P(A)+P(B)-P(AB)
Events A
and B are independent if ?
Is it same as disjointness?
What about 3 events?
What about n events?
Under
the load of F, the probabilities of
failure of the indivi

Dr. Ming Yang
Process Engineering
Office: IIC 1017
Email: [email protected]
One
part of the course deals with how to
extract valuable/useful information from
uncertainty real-world data.
The other part of the course deals with
how to make decision under unce

ENGI 9411
Fall 2014
A
function from sample space to the real
line
A numerical summary of an aspect of the
experiment
Types
Discrete random variables
Continuous random variables
Hybrids
Cumulative
Distribution Function
Probability Mass Function: P(

ENGI 9411
Fall 2014
Chevalier
de Mere, a French gambler
posed a question to his friend Blaise
Pascal:
Why the likelihood of one double-six in
24 tosses of a pair of dice is different
from that of one six in 4 tosses of a die
The correspondence about thi

Assignment 3
Engineering 9411
Due date: Nov. 8th, 2016
1. The following natural gas distribution network contains five shut-off valves
configured as shown. Valves 1-4 have a probability of 0.012 of failing open and a
probability of 0.15 of failing short.

Assignment 2
Engineering 9411
Due date: Oct. 16th, 2016
1. In considering the safety of a building, the total force acting on the columns of the
building must be examined. This would include the effects of the dead load D
(due to the weight of the structu

Assignment # 6: Physical reliability models
Due Date: 31 July 2014
1. The time to failure of a drill bit is lognormal with s = 1.43. From field data the median
life of the bit has been found to depend on the hardness and the density of the material
being

Assignment 1
Engineering 9411
Due date: Oct.1st, 2015
Question 1:
In most engineering studies, major sources of uncertainty can be grouped into four
categories:
a) Uncertainty due to natural variability;
b) Uncertainty due to error in parameter estimation

X
Random Value Generated for Sketching Distribution
y
PDF
CDF
0.500747686 1.649954 0.36733 0.393922665
0.563758336 1.757264 0.323836 0.430933702
0.454842054 1.575924 0.402651 0.365451816
0.542093122 1.719602 0.338177 0.418470235
0.485450571 1.624907 0.378

Probabilistic Methods in Engineering
Engineering 9411
Final Examination
Vijayakumar Ramamoorthy
1. Aggregates for a highway pavement are extracted from a gravel pit. Based on experience with
the material from this area, it is known that the probabilities

Question-2 - Sketch of the Given Distribution
Fixing the X as the random variable(RV) that is exponentially distributed
x( Exponentially
RV
distributed)
f(x)
y
PDF
CDF
0.391906
0.4462148799 0.640046 1.562387 0.409659 0.359954
0.970876
0.5969305842 0.55049