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Probability Methods for Cost Uncertainty Analysis

A Systems Engineering Perspective, Second Edition

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## Book Description

**Probability Methods for Cost Uncertainty Analysis: A Systems Engineering Perspective, Second Edition** gives you a thorough grounding in the analytical methods needed for modeling and measuring uncertainty in the cost of engineering systems. This includes the treatment of correlation between the cost of system elements, how to present the analysis to decision-makers, and the use of bivariate probability distributions to capture joint interactions between a system’s cost and schedule. Analytical techniques from probability theory are stressed, along with the Monte Carlo simulation method. Numerous examples and case discussions illustrate the practical application of theoretical concepts.

While the original chapters from the first edition remain unchanged, this second edition contains new material focusing on the application of theory to problems encountered in practice. Highlights include the use of GERM to build development and production cost estimating relationships as well as the eSBM, which was developed from a need in the community to offer simplified analytical alternatives to advanced probability-based approaches. The book also lists the major technical works of the late Dr. Stephen A. Book, a mathematician and world-renowned cost analyst whose contributions advanced the theory and practice of cost risk analysis.

## Table of Contents

*Theory and Foundations*Uncertainty and the Role of Probability in Cost Analysis

Introduction and Historical Perspective

The Problem Space

Presenting Cost as a Probability Distribution

Benefits of Cost Uncertainty Analysis

**Concepts of Probability Theory **

Introduction

Sample Spaces and Events

Interpretations and Axioms of Probability

Conditional Probability

Bayes’ Rule

**Distributions and the Theory of Expectation **

Random Variables and Probability Distributions

Expectation of a Random Variable

Probability Inequalities Useful in Cost Analysis

Cost Analysis Perspective

**Special Distributions for Cost Uncertainty Analysis **

Trapezoidal Distribution

Beta Distribution

Normal Distribution

Lognormal Distribution

Specifying Continuous Probability Distributions

**Functions of Random Variables and Their Application to Cost Uncertainty Analysis **Introduction

Linear Combinations of Random Variables

Central Limit Theorem and a Cost Perspective

Transformations of Random Variables

Mellin Transform and Its Application to Cost Functions

**System Cost Uncertainty Analysis **

Work Breakdown Structures

Analytical Framework

Monte Carlo Simulation

**Modeling Cost and Schedule Uncertainties: An Application of Joint Probability Theory **Introduction

Joint Probability Models for Cost-Schedule

Summary

*Practical Considerations and Applications*Elements of Cost Uncertainty Analysis: A Review

Introduction

Cost as Probability Distribution

Monte Carlo Simulation and Method of Moments Distribution

Summary

**Correlation: A Critical Consideration **

Introduction

Correlation Matters

Valuing Correlation

Summary

**Building Statistical Cost Estimating Models**

Introduction

Classical Statistical Regression

General Error Regression Method

Summary

**Mathematics of Cost Improvement Curves **

Introduction

Learning Curve Theories

Production Cost Models Built by Single-Step Regression

Summary

**Enhanced Scenario-Based Method**

Introduction

Nonstatistical eSBM

Statistical eSBM

Historical Data for eSBM

Summary

**Cost Uncertainty Analysis Practice Points **

Treating Cost as a Random Variable

Risk versus Uncertainty

Subjective Probability Assessments

Subjectivity in Systems Engineering and Analysis Problems

Correlation

Capturing Cost-Schedule Uncertainties

Distribution Function of a System’s Total Cost

Benefits of Cost Uncertainty Analysis

Establishing a Cost and Schedule Risk Baseline

Determining Cost Reserve

Conducting Risk Reduction Trade-Off Analyses

Documenting the Cost Uncertainty Analysis

Management Perspectives

**Collected Works of Dr. Stephen A. Book **

Textbooks

Journal Publications

Conference Presentations and Proceedings

Appendices

Index

*Exercises and References appear at the end of each chapter.*

## Author(s)

### Biography

**Paul R. Garvey** is Chief Scientist for the Center for Acquisition and Management Sciences at The MITRE Corporation. He has extensive experience in the theory and application of risk-decision analytic methods to operations research problems in the system sciences domains. He is the author of the CRC Press books *Advanced Risk Analysis in Engineering Enterprise Systems* (with C. Ariel Pinto) and *Analytical Methods for Risk Management*. He earned an A.B. and M.Sc. in pure and applied mathematics from Boston College and Northeastern University and a Ph.D. in engineering systems risk analysis from Old Dominion University.

**Stephen A. Book** (1941–2012) was a Distinguished Engineer in the Systems Engineering Division at the Aerospace Corporation, chief technical officer at Management Consulting and Research (MCR), and emeritus professor of mathematics at California State University, Dominguez Hills. A world-renowned cost analyst, Dr. Book produced innumerable contributions to the field and made his work accessible to professionals from a variety of academic and technical backgrounds. He earned an A.B., M.A., and Ph.D. in mathematics from Georgetown University, Cornell University, and the University of Oregon, respectively.

**Raymond P. Covert** is the founder of Covarus LLC, a boutique consulting firm specializing in engineering and economic modeling. He has over 30 years of experience in aerospace and defense engineering and is the author of a series of books on cost and schedule estimating. He has published more than 60 technical and tutorial presentations. He earned an Sc.B. in aeronautical and astronautical engineering from the Massachusetts Institute of Technology and an M.S. in electrical engineering from Loyola Marymount University.

## Reviews

Praise for the First Edition:"Sound theoretical basis, fine-tuned by empirical evidence, and focused like a laser on the application of performing cost risk analysis on complex systems … after teaching from a collection of papers, I’m delighted to finally find this well-written text."

—Daryl J. Hauck, Ph.D., Assistant Professor, Ohio"Paul Garvey has done a tremendous job taking a technical subject and producing a readable, interesting, and informative primer. … strongly recommend[ed] … to all professional cost analysts, both for its readability and its insights … also recommend[ed] … to anyone who is in the position of making decisions based on cost estimates."

—Phalanx, The Bulletin of Military Operations Research"… does a very thorough job of explaining probability methods in cost uncertainty analysis in mathematical terms."

—International Cost Engineering Council, 2001"This book focuses on the development of a structured approach to quantifying the uncertainty of cost estimates, backed by a great deal of mathematical rigor."

—INCOSE Insight, 2001