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ENGINEERING SYSTEMS & DECISION ANALYSIS (CIVE3066) COURSE INTRODUCTION Instructor Nguyen Tuan Thanh LE (thanhlnt@tlu edu vn) Based on the CIVE203 Engineering system and decision analysis Colorado stat[.]

Instructor:

Nguyen-Tuan-Thanh LE (thanhlnt@tlu.edu.vn)

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA

& Role of statistics in engineering – California State University, USA

COURSE OBJECTIVES

▪ Prepare you to effectively use models and statistics in your courses and career using MatLab/Octave and GIS skills

▪ Provide you with the capabilities of:

▪ Understanding the concepts of mathematical modeling and statistical data analysis as

applied to civil engineering systems.

▪ Estimating parameters for various statistical distributions, determining which distribution

best describes a set of data and to generate random samples from those distributions.

▪ Demonstrating the proper application of confidence limits and hypothesis testing to

examples from civil engineering systems.

▪ Demonstrating the proper application of simple linear or multiple regression for building

empirical models of engineering and scientific data.

▪ Demonstrating the use of Geographic Information Systems (GIS) for spatial data

collection, organization, and analysis.

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EXAMS AND GRADING

▪ The course will include two multiple choice quarterly, a midterm and

a comprehensive final examination

▪ Grading will be based on the following components:

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▪ Assigned weekly on the piazza forum

▪ Students submit homeworks on piazza with a zip files including all

necessary files The name of the zip file as well as the title of the

email should be: CIVE3066_59NKN_HWK n_Student’s name

▪ where n is the number of the current homework

▪ for example: CIVE3066_59NKN_HWK1_NguyenVanA

▪ Late homework is not accepted

▪ Solutions are posted on piazza or presented in class after due date

▪ Must be your own work Copied work will have the note 0

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GENERAL CLASS POLICIES

Students are expected to:

▪ Attend regularly

▪ Ask questions

▪ If you do not understand what the lecturer is saying or if you detect any errors

▪ Access the course forum piazza regularly

▪ Respect the lecture time

▪ Turn off or silence your cell phones before the start of class

▪ Respect assignment deadlines: late submissions will not be accepted.

▪ Be honest:

▪ Violations of the academic integrity policies may include: cheating, plagiarism, aiding

academic dishonesty, fabrication, lying, bribery, and threatening behavior.

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7 Decision making for a single sample

8 Building empirical models

9 Simple linear regression

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RECOMMENDED TEXTBOOKS

▪ Engineering Statistics-Fifth Edition, Montgomery, D.C., G.C Runger and N.F

Hubele, John Wiley & Sons, Inc., 2011.

▪ Probability Concepts in Engineering- Second Edition, Ang, A and W Tang,

John Wiley & Sons, Inc.

▪ Geographic Information Systems and Science, Longley, P., John Wiley & Sons,

Inc.

▪ Applied Numerical Methods with MATLAB for Engineers and Scientists,

Chapra, S.C., McGraw Hill.

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OTHER MATERIALS

▪ MATLAB Statistics Toolbox, MathWorks Inc.

▪ MATLAB Curve Fitting Toolbox, MathWorks Inc.

▪ Numerical Computing with MATLAB , Moler, C.

▪ Think Stats: Exploratory Data Analysis in Python , Allen B Downey, 2014.

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THE SCIENTIFIC METHOD

▪ Your sample is the 100 chosen people, while the population is all

the people at that match

▪ Sample: a selection taken from a larger/total group (the

“Population”) so that you can examine it to find out something

about the larger/total group [1]

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA

[1] https://www.mathsisfun.com/definitions/sample.html 4

DATA SAMPLING (2/2)

▪ Data sampling is a statistical analysis technique

representative subset of data points

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA

[2] http://searchbusinessanalytics.techtarget.com/definition/data-sampling 5

DATA COLLECTION:

SAMPLE DESIGN – STRATEGY

▪ Non-probability Sampling : selecting samples based on the subjective

judgment of researchers rather than random selection

▪ Haphazard Sampling (Convenience Sampling)

▪ Judgment Sampling (Purposive/Expert Sampling)

▪ Probability Sampling : sample are chosen using a method based on the

theory of probability

▪ Simple Random Sampling

▪ Stratified Random Sampling

▪ Clustering Sampling

▪ Multistage Sampling

▪ Systematic Sampling

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NON-PROBABILITY SAMPLING:

HAPHAZARD/CONVENIENCE

SAMPLING

and recreate true randomness.

▪ Example: you stand on a busy corner during rush hour and interviewing

people who pass by.

unbiased estimates

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 7

NON-PROBABILITY SAMPLING:

JUDGMENT/PURPOSIVE/EXPERT SAMPLING

credibility

(with respect to attributes and representation of a population) to

participate in research study.

completely accessible so that sample selection bias is not a problem.

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PROBABILITY SAMPLING:

SIMPLE RANDOM SAMPLING (1/3)

▪ Each of the population units has an equal chance of being

selected for measurement.

other units

locations haphazardly.

population does not contain major trends, cycles, or

patterns.

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PROBABILITY SAMPLING:

STEPS

1 A list of all the members of the population is prepared

initially and then each member is marked with a specific

number (for example, there are N members then they will be

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 11

Method of lottery

Excel Functions:

• RANDBETWEEN(a,b)

• RAND()

PROBABILITY SAMPLING:

SIMPLE RANDOM SAMPLING (3/3) – EXAMPLE

100 from them.

▪ Step 1: Make a list of all the employees working in the organization

▪ As mentioned above there are 500 employees in the organization, the list must contain

500 names).

▪ Step 2: Assign a sequential number to each employee (1,2,3…500) This is

your sampling frame (the list from which you draw your simple random sample).

▪ Step 3: Figure out what your sample size is going to be.

▪ In this case, the sample size is 100

▪ Step 4: Use a random number generator to select the sample, using your

sampling frame (population size) from Step 2 and your sample size from Step 3

▪ In this case, your sample size is 100 and your population is 500, so generate 100

random numbers between 1 and 500.

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PROBABILITY SAMPLING:

▪ The target population is divided into non-overlapping,

homogeneous sub-regions/groups called strata (statum) to obtain

a better estimation of the mean of the population.

▪ Age, socioeconomic divisions, nationality, religion, educational achievements, … fall under stratified random sampling.

▪ Samples within each strata is selected by Simple Random

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 16

PROBABILITY SAMPLING:

STRATIFIED RANDOM SAMPLING (2/2) - EXAMPLE

▪ Let’s consider a situation where a research team is seeking

opinions about religion amongst various age groups

▪ Instead of collecting feedback from 326,044,985 U.S citizens, random samples of around 10000 can be selected for research

▪ These 10000 citizens can be divided into strata according to age,i.e, groups of 18-29, 30-39, 40-49, 50-59, and 60 and above

▪ Each stratum will have distinct members and number of members.

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PROBABILITY SAMPLING:

CLUSTERING SAMPLING

▪ The target population is divided into clusters of

individual units

in the chosen clusters are measured

▪ Useful when population units cluster together and each unit in the randomly selected cluster can be measured

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 18

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 19

Cluster Sampling

▪ Elements of a population are randomly

selected to be a part of groups (clusters).

▪ Members from randomly selected clusters are

a part of this sample.

▪ Homogeneity is maintained between clusters

▪ Heterogeneity is maintained with the clusters.

▪ The clusters are divided naturally.

▪ The key objective is to minimize the cost

involved and enhance competence.

Stratified Random Sampling

▪ The entire population is divided into even segments (strata).

▪ Individual components of the strata are randomly considered to be a part of sampling units.

▪ Homogeneity is maintained within the strata.

▪ Heterogeneity is maintained between strata.

▪ The strata division is primarily decided by the researchers or statisticians.

▪ The key objective is to conduct accurate sampling along with properly represented population.

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CLUSTER SAMPLING VS

STRATIFIED SAMPLING

PROBABILITY SAMPLING:

MULTISTAGE SAMPLING

▪ The target population is divided into primary units

(clusters)

▪ Then, a set of primary units is selected by using

Simple Random Sampling and each is randomly

sub-sampled

▪ Needed when measurements are made on

sub-samples of the field sample

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 21

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 22

PROBABILITY SAMPLING:

▪ The elements are chosen from a target population by selecting a

random starting point and selecting other members after a fixed

‘ sampling interval ’.

▪ Sampling interval is calculated by dividing the entire population

size by the desired sample size.

▪ Example:

▪ A local NGO is seeking to form a systematic sample of 500

volunteers from a population of 5000,

▪ They can select every 10 th person in the population to

systematically form a sample

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Linear Systematic Sampling Circular Systematic Sampling

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PROBABILITY SAMPLING:

1 Arrange the entire population in a classified sequence

2 Select the sample size (n)

3 Calculate sampling interval (k) = N/n

4 Select a random number between 1 to k (including k)

5 Add the sampling interval (k) to the chosen random number to

add the next member to a sample and repeat this procedure to

add remaining members of the sample

6 In case k isn’t an integer, can select the closest integer to N/n.

1 Calculate sampling interval (k) = N/n (If N = 11 and n

= 2, then k is taken as 5 and not 6)

2 Start randomly between 1 to N

3 Create samples by skipping through k units every time until you select members of the entire population

4 In case of this systematic sampling method, there will

be N number of samples, unlike k samples in the linear systematic sampling method

if N = 7, n = 2, k=3, the samples

will be: ad, be,

ca, db and ec.

THE SCIENTIFIC METHOD

2 DESCRIPTIVE STATISTICS

▪ Descriptive statistics are statistical measures used to

describe a set of samples (or observations)

▪ Three kinds of descriptive statistics:

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 26

DESCRIPTIVE STATISTICS:

CENTRAL TENDENCY - MODE

▪ The value has the largest number of observations

▪ MATLAB Syntax: M = mode(X); M = mode(X, dim);

▪ Description

▪ M = mode(X)

▪ If X is a vector, M is the sample mode (the most frequently occurring value) of X

▪ If X is a matrix, M is a row vector containing the mode of each column of that matrix

▪ When there are multiple values occurring equally frequently, mode returns the smallest

of those values

▪ M = mode(X, dim) computes the mode along the dimension dim of X

▪ dim = 1 or 2

▪ 1: return a row vector (default)

▪ 2: return a colum vector

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≥ ≥

Normalize with N-1, provides the square root

of the best unbiased estimator of the variance

Normalize with N, this provides the square root

of the second moment around the mean

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3 DATA PROCESSING

▪ Data processing involves verification, coding, classification

& tabulation of data

▪ Verification: verify to ensure that the data is accurate

▪ Coding: the verify data is converted into machine readable form so

that it can be processed through computer

▪ Classification: data are classified on the basis of common

characteristics which may be qualitative or descriptive &

quantitative or numericals

▪ Tabulation: it is concise, logical & orderly arrangement of data in a

columns & rows

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 39

MISSING DATA (1/2)

usually represented by the special value NaN, which is

Not-a-Number.

1) if any element of the vector is nonzero

Based on the CIVE203 - Engineering system and decision analysis - Colorado state University, USA 40

▪ X=X(~isnan(X)) : remove NaNs from X

▪ X(isnan(X)) = [] : remove NaNs from x

▪ M(any(isnan(M),2),:)=[] : remove any rows containing NaNs

M= NaN 6 10 2

8 1 4 2

8 6 7 2

SCATTER PLOT

▪ scatter(X, Y) : create a scatter plot with circles at the

locations specified by the vectors X and Y

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TIME SERIES PLOT

▪ plot(X) : plot the time series data X against time.

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BAR CHART

▪ bar(Y) : create a bar graph with one bar for each element in Y

▪ bar(X, Y) : draws the bars of Y at the locations specified in X

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STEM PLOT

▪ stem(Y) : plot the data sequence Y as stems that extend from the

baseline along the x-axis

▪ stem(X, Y) : plot the data sequence Y at values specified by X

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▪ boxplot(X) : create a box plot of the data in X

▪ boxplot(X1, X2, X3) : create a box plot for each group of data X1, X2, X3

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• Model: an idealized version of how the world works

• Data: collected observations

PROBABILITY VS STATISTICS (2/2)

▪ Probability:

▪ Statistics:

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1 Basic concepts

Based on Probability and statistics for engineers – Radim Bris – Technical University of Ostrava and

Probability and statistics for enginneers and scientists – Eight Edition – Ronald E Walpole and Raymond H Myers 4

1 BASIC CONCEPTS

Examples of Probability

▪ Flip a coin N times, the proportion of heads against the number of flips

▪ The probability of a certain size of flood flow occurring in any one year

▪ The probability of a certain kind of vehicle crossing a certain point on a road

Probability theory

▪ Probability is a measure of the likelihood of a random phenomenon or chance

behavior

▪ Probability allows to model the frequency of realization of random events.

▪ Probability theory is a mathematical framework for computing the probability of

complex events

Based on Probability and statistics for engineers – Radim Bris – Technical University of Ostrava and

Probability and statistics for enginneers and scientists – Eight Edition – Ronald E Walpole and Raymond H Myers 5

SOME DEFINITIONS

▪ Probability experiment (ε): an action or trial through which specific

results (counts, measurements or responses) are obtained

▪ Outcome (ω): the result of a single trial (a probability experiment)

▪ Sample space (Ω): the set of all possible outcomes of a probability

experiment

▪ Event (A): is a subset of the sample space, consisting of one or more

outcomes

▪ We have: ω ∊ Ω and A ⊂ Ω

Based on Probability and statistics for engineers – Radim Bris – Technical University of Ostrava and

Probability and statistics for enginneers and scientists – Eight Edition – Ronald E Walpole and Raymond H Myers 6