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Introduction

Dr. Jerrell T. Stracener, SAE Fellow

Leadership in Engineering

EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS

Systems Engineering ProgramDepartment of Engineering Management, Information and Systems

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Relationship Between Probability & Statistics

Population Sample

Probability

DescriptiveStatistics

InferentialStatistics

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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 ofpossible 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 canbe combined to obtain other probabilities.

- What are the rules of probability?

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Objective

Introduction to fundamental 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 theproblem 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

Visualize

Relate to Physical

Develop Diagram

/Flow chart

Identify Solution Approaches

Establish Ground Rules and Assumptions

Revisit Problem and Define Objective

Down-select to preferred Solution Approach

Solve Problem and Perform Check

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

• Introduction• The Scientific Method• The Role of the People involved in the Analysis• Explanation of established procedures• The Template• Examples

Outline

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INTRODUCTION

Decision Making = choosing among alternatives

Objective / Question

Analyst (analysts, scientists, engineers, etc)

Models (analytical, simulations, etc.)

Data / Assumptions

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The product of decision makers

Choices will be made with or without analysis

Key pillars of analysisHelping the decision maker understand problems and

candidate solutions

The foundations of credible analysis

Tools, techniques, and infor-mation surrounding the art of timely, informative support to

decision makers

Role of Analysis

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INTRODUCTION

The EssentialIngredients of

Analysis

Objective/Question

Analyst

Model(s)Data/Assumptions

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THE SCIENTIFIC METHOD

• 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• Exercise “tool(s)”• Analyze results• Report Results

Typically we jump to these steps

Typically we spend the least amount of our time in this step

“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

• 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? -

• 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– 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

• Initial Diagnosis– Identify critical factors– What the principle decisions are– What the MOEs( Measures of Effectiveness) are– Tradeoffs to compare alternatives

• Problem Elements– 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

Principles of Management Science - Wagner

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EXPLANATION OF ESTABLISHED PROCEDURES

• Decision Objectives - goal of the decision• Problem Context

– Stakeholders– Triggers– Influences

• Problem Boundaries– Timeframe– Rule sets– Facts– Assumptions

• Analytic Objectives

Naval War College Pub

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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