EDD 112 Final SUNY Binghamton University

What are statistics?

The collection, organization, analysis, and interpretation of data

What are the 2 types of statistics?

descriptive and inferential

What does the frequency distribution provide?

A compact summary of data by showing how many units fall into each attribute of a variable

What is a histogram a pictorial summary of?

Descriptive statistics

Measures of central tendency is descriptive statistics?

Mean
Median
Mode
Quartiles
Percentiles
Trimmed means

What are the units of variance?

Units squared

Sample variance

Measure of variability based on derivation from the mean

Sample standard deviation

Square root of the variance, denoted by s

What must you have to calculate population variance?

Every value of the population

Inferential statistics

Focuses on drawing conclusions about a population based on sample info

Population

Consists of all individuals or objects of a particular type

Sample

Subset of the population

Why do we use Statistics?

To acquire info
Draw conclusions about an entire population

What does Simio use stats to do?

Evaluate processes

When choosing between standard deviation and variation, what do people tend to choose and why?

SD bc the units are more intuitive

Random variable

Any rule that assigns a numerical value to each outcome of an experiment

Random variable types

Discrete and continuous

2 types of probability distributions

Probability density functions
Discrete probability density function

Probability density functions

A function p(x) or f(x) that relates the values of the occurance graphically or as an equation

Are probability density function continuous or discrete?

Can be both

What condition does discrete probability function satisfy?

The probability that x can take a specific value is p(x)
p(x) is + or 0 for all real x
The sum of p(x) over all positive values is 1

"There's no sense being exact about something if you don't even know what you're talking about"

John von Neumann

What do requirements describe?

Necessary functions and features of a system we are able to conceive, design, implement, and operate

How are requirements often organized?

Hierarchially

At a high level, what do requirements focus on?

What should be achieved, not how to achieve

Are requirements specified at every level?

Yes

What do requirements specify the design in terms of?

What the design must accomplish
What constraints are satisfied

What forms the backbone of systems engineers?

Requirements

What do system engineers do?

Delegate requirements to successively lower level subsystems and components, then verifies that requirement are met at each level

What do requirements provide the basis of?

Design
Implementation
Verification
Operation
Maintenance

Waterfall model

Requirements
Design
Implementation
Verification
Maintenance

Objectives of requirements analysis

Identification and expression of verificable requirements that state user needs in clear, relevant terms that enable the system to be developed
Maintain project scope

What does requirements analysis start with

Voice of the customer

When validity is checked, what questions are asked?

Is this a good requirement?
Is it consistent with higher level requirements?
Is it achievable given lower-level requirements

Bottom up constraints

Tech and physics
Vendor capabilities
Quanta of size, mass, precision

What does verification include?

Tests
Inspection
Analysis

What is verification without requirements?

Wasted effort

What do requirements without verification prevent?

Development cycle from being complete

Overview of the Requirements Engineering Process

Capture source requirements
Iteratively create functional and performance requirements
Allocate requirements and establish traceability
Develop specs of requirements via a Verification Cross-Reference Matrix

What does a Verification Cross-Reference matrix map?

Each requirement to a verification method

General categories of requirements

Functional
Performance
Interface
Environmental

What do functional requirements define?

What functions are needed to be done to accomplish the mission objective

What do performance requirements define?

How well the system needs to perform functions

Ittities requirement types described in the SE Handbook include

human factors
reliability and maintainablity requirements
safety requirements

What are constraints?

Requirements that can't be traded off with respect to cost, schedule, or performance

What are customer requirements?

Product expectations
Mission objectives
Operational concerns
Measures of effectiveness and suitability
May require careful analysis to extract functions
Generally provide success criteria

Functional requirements

Task the system must accomplish
Top-level functions for functional analysis

Performance requirements

Quantitative or qualitative measures of system performance or functions

What are design requirements derived from?

Design process specs
Internal "best practices"

Derived requirements

Any requirements flowed down from a higher level

Allocated requirements

Any requirement established by dividing or allocating a higher-level requirement into more than one requirement at a lower level

Interface requirements

Requirements that specify the function or structural interfaces among subsystems

Verification requirements

Requirements that specify the way in which verification must proceed

Characteristics for each requirement statement

Unambiguous
Isolated/Singular
Clear/Consistent
Correct
Measurable/Verifiable
Feasible
Flexible

Characteristics for pairs and sets of Requirement Statements

Absence of redundancy
Consistency
Completeness
Absence of conflicts

What words/phrases do requirements avoid to be unambiguous?

Reasonable
Acceptable
Minimize
Where applicable

How can requirements be verified?

Tests
Analysis
Inspection

Matrix

Rectangular array of numbers, symbols, or expressions arranged in rows and columns

What are the individual items in a matrix?

Elements or entries

Row vector

1xn

Column vector

nx1

Square matrix

nxm

What is cryptography?

Practice and study of means of keeping communication secure

Who is the professor in the Electrical and Computer Engineering Department that does research in cryptography?

Dr. Scott Craver

Conditions for a matrix to have an inverse

Square matrix
Determinant does not equal zero

Adjoint method

A^-1=(1/det(A))(adj(A))

What is the adjoint of a matrix found as?

Transpose of the Cofactor Matrix

Once all elements of the cofactor matrix have been found, how do we calculate the Adjoint?

Transpose of matrix

Examples of mechanical engineering applications of matrices

Mechanical Vibrations
Finite Element Analysis

What is finite element analysis?

Breaking down the physical system into many small finite elements, developing the equations of motion for each element, and then solving all equations simultaneously

Leonhard Euler

Swiss mathematician

What gives results consistent with simulation

Complex impedances in circuit analysis

Complex impedance examples

Capacitors and inductors

Real impedance example

Resistors

How are capacitors and inductors represented

Imaginary complex #s

How are resistors represented

Real parts of complex #s

What does impedance describe

Circuit element opposition to current flow

When are vectors used in mechanical engineering?

Free body diagrams
Statics

When are vectors used in electrical engineering

Analysis of electric and magnetic fields
Electromagnetics

When are vectors used in BME

thermodynamics

When are vectors used in ISE

industrial machinery
industrial automation
statics

Scalars

Representative of a quantity that can be completely represented by magnitude alone

Scalar examples

Mass
Volume
Speed

Vectors

Representative of a quantity that has both magnitude and direction

Vector examples

Force
Velocity

Is vector addition cummutative?

Yes

Divergence

Represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point

Gradient

Generalization of the concept of derivative of a function in one dimension to a function in several dimensions

Curl

Represents the rotation of a vector field

When the sine wave delays in time, what is there?

A phase lag

When the sine wave advances in time, what is there?

A phase lead

What is the phase angle sometimes called?

Phase shift

What is amplitude modulation used to do in communications?

Transmit info using a carrier wave

Modulation product

Multiply carrier wave and the information wave

Fourier series

Summation of sinewaves, each component 10 degrees higher frequency than the previous

Applications of the Fourier Series

Electrical engineering
Vibration analysis
Optics
Acoustics
Signal processing
Image processing

Verification

Confirmation that a component, sub-system, or full system meets identified requirements

Validation

Confirmation that a component, sub system, or full system appropriately meets its design function or intended use

Validated key word

Implies

Verification key word

And