Transcript Introduction - Lyle School of Engineering

Systems Engineering Program
Department of Engineering Management, Information and Systems
EMIS 7370/5370 STAT 5340 :
PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS
Introduction
Dr. Jerrell T. Stracener, SAE Fellow
Leadership in Engineering
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Relationship Between Probability & Statistics
Probability
Population
Sample
Inferential
Statistics
Descriptive
Statistics
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Probability
• What is it?
• How can it be applied to engineering?
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Probability
The term probability refers to the study of randomness
and uncertainty.
The Theory of Probability provides methods for
quantifying the chances, or likelihood, associated with the
various outcomes in any situation in which one of a number of
possible outcomes may occur.
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Basic Questions:
(1) First, there is a question of what we mean when we say
that a probability is 0.82, or 0.25.
- What is probability?
(2) Then, there is the question of how to obtain numerical
values of probabilities, i.e., how do we determine that a certain
probability is 0.82, or 0.25.
- How is probability determined?
(3) Finally, there is the question of how probabilities can
be combined to obtain other probabilities.
- What are the rules of probability?
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Objective
Introduction to basic probabilistic and statistical techniques for
application to engineering and research for:
– modeling and analysis of variability
– analysis of data
to impact the decision making process
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Purpose of Analysis
To impact the decision-making
process
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The Analysis Process
1. Define the problem and formulate an objective
2. Identify the analysis options for accomplishing
the objective and down-select to the preferred
option.
3. Perform the analysis and draw conclusions
4. Present the analysis results, both technically
and from the layperson perspective
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Problem Solving Approach
• Define the problem
• Visualize
• Diagram
• Review the problem definition & objective
• Formulate possible alternates for solving the
problem and down select to the preferred method
• Solve the problem
• Review the results and prepare report
• Present report
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Analysis Process
Define
Problem and
Requirements
Identify Solution
Approaches
Down-select to
preferred Solution
Approach
Visualize
Develop Diagram
Relate to Physical
/Flow chart
Establish Ground
Rules and
Assumptions
Solve Problem
and Perform
Check
Revisit Problem
and Define
Objective
Review Results
and Draw
Conclusions
Present
Results
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“STEP #1 OF THE
SCIENTIFIC METHOD:
DEFINING THE PROBLEM”
by
Roy E. Rice, Ph.D., P.E.
AF OR FAM Course
25 Apr 2005
Selected Charts
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DEFINING THE PROBLEM
Outline
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Introduction
The Scientific Method
The Role of the People involved in the Analysis
Explanation of established procedures
The Template
Examples
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INTRODUCTION
Role of Analysis
The product of
decision makers
The foundations of
credible analysis
Tools, techniques, and information surrounding the art of
timely, informative support to
decision makers
Ensure trackability/
traceability
Helping the decision maker
understand problems and
candidate solutions
Establish
meaningful
measures
Key pillars of analysis
Define issues/
questions
Choices will be made with or
without analysis
Ensure adequate
range of
alternatives
Decision Making =
choosing among alternatives
Objective / Question
Analyst (analysts, scientists, engineers, etc)
Models (analytical, simulations, etc.)
Data / Assumptions
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INTRODUCTION
Objective/Question
Data/
Assumptions
The Essential
Ingredients of
Analysis
Model(s)
Analyst
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THE SCIENTIFIC METHOD
“Operations research is a scientific method of providing executive
departments with a quantitative basis for decisions regarding the operations
under their control.” -- Morse and Kimball
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Define the Problem
Develop Alternatives
Develop Criteria to distinguish among alternatives
Develop “measures” of the criteria
Determine Analytic Methodology (to include DOE)
Determine “tool(s)” to execute the methodology
Gather data
Typically we jump to
Exercise “tool(s)”
these steps
Analyze results
Typically we spend the
least amount of our time
Report Results
in this step
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DEFINE THE PROBLEM
• Step 1
– “Define Problem”
• Step 1a (Roy’s Rule)
– “Define the Problem again…because you didn’t do it right
the first time!”
• Step 1b (Vince Roske’s Rule)
– “First find out what the question is - then find out what
the real question is!”
• EXAMPLE: Close Air Support Study in J8
“It often occurs that the major contribution of the operations research
worker is to decide what is the real problem.” -- Morse and Kimball
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DEFINE THE PROBLEM
- WHY? •
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•
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Perfectly right answer to the totally wrong question!
Probably waste resources
Probably lose Credibility
NATO Code Of Best Prictices - DRAFT
– “In the initial problem formulation iteration, it is critical to
begin with an understanding of the REAL problem rather than
a determination to apply readily available tools, scenarios, and
data.”
– “Explicit problem formulation must precede construction of
concepts for analysis or method selection…Proper resourcing
of problem formulation activities will improve the overall
efficiency and quality of the study.”
– “An understanding of the decisions to be supported by the
analysis and the viewpoints of the various stakeholders is
essential to clarifying the study issues.”
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THE ROLE OF THE PEOPLE INVOLVED IN
PROBLEM DEFINITION
• The Decision Maker
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Communicate the “context” of the Problem
“Buy into” the Problem and Solution Approach
Provide “Heading Checks”
Have Open Door
Commitment vs. Participation - “ham & eggs”
• The Mid-level Manager
– Be a Conduit
– “What does your FINAL chart look like?”
– Must understand analysis - what it can/cannot do
• The Analyst
– Articulate the Problem back to D.M.
– Must put himself/herself in the D.M.’s shoes
Problem Definition is an Iterative Process
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EXPLANATION OF
ESTABLISHED PROCEDURES
Principles of Management Science - Wagner
• Initial Diagnosis
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Identify critical factors
What the principle decisions are
What the MOEs( Measures of Effectiveness) are
Tradeoffs to compare alternatives
• Problem Elements
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Controllable or decision variables
Uncontrollable variables
Restrictions or constraints on the variables
Objectives for defining a good or improved solution
“Confines” of the analysis - multifold impacts
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EXPLANATION OF
ESTABLISHED PROCEDURES
Naval War College Pub
• Decision Objectives - goal of the decision
• Problem Context
– Stakeholders
– Triggers
– Influences
• Problem Boundaries
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Timeframe
Rule sets
Facts
Assumptions
• Analytic Objectives
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EXPLANATION OF
ESTABLISHED PROCEDURES
• Rice’s Method (from Dr. Bill Lesso, University of Texas at
Austin)
Given:
The problem is to:
By choice of:
Subject to:
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RICE’S METHOD
Given: set the environment; state
your assumptions
The problem is to: clear statement
of the specific problem to be solved
By choice of: determine the
decision variables
Subject to: determine the
constraints and restrictions
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RICE’S METHOD
Given:
- what is the timeframe of the study?
- what scenario(s) are applicable?
- what alternatives are to be used?
- what are “fixed” parameters?
- who are the players?
- what are the threats?
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RICE’S METHOD
Given:
The problem is to:
- not “to analyze” or “to study”
- not a statement of fact (e.g., “we have a
pilot shortage”)
- address the causes not the symptoms
- what are you really trying to quantify or
measure?
- probably related to operational
objectives
- what...
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RICE’S METHOD
Given:
The problem is to:
By choice of:
- what are the decision variables?
- what does the decision maker get to
“play with”?
- what does he/she have control over?
- what...
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RICE’S METHOD
Given:
The problem is to:
By choice of:
Subject to:
- constraints - hard; inviolable (e.g., distances,
24 hours in a day, ramp space)
- restrictions - man-made (e.g., start times)
- what are the constraints on the variables?
- what might you want to perform sensitivity
analysis on?
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SUMMARY
• Follow the Scientific Method
• Step 1: Problem Definition is the most critical step
• Problem Definition is an iterative process
– Must get Decision Maker commitment
• Procedures:
– NATO C2 COBP
– Rice’s Method
“In section 3.4.4 is reported a case where it was nearly decided that it was not
worth while to put antiaircraft guns on merchant vessels because they did not
shoot down enemy planes. It took an operations research worker to point out
that, even though the enemy planes were not shot down, the antiaircraft guns
were valuable because they decreased the accuracy of the enemy planes enough
to lessen the chance that the merchant vessel be sunk..” -- Morse and Kimball
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