Probability Methods for Cost Uncertainty Analysis: A Systems Engineering Perspective, Second Edition, 2nd Edition (Hardback) book cover

Probability Methods for Cost Uncertainty Analysis

A Systems Engineering Perspective, Second Edition, 2nd Edition

By Paul R. Garvey, Stephen A. Book, Raymond P. Covert

Chapman and Hall/CRC

502 pages | 171 B/W Illus.

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Hardback: 9781482219753
pub: 2015-12-22
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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.


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

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


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


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


Joint Probability Models for Cost-Schedule


Practical Considerations and Applications

Elements of Cost Uncertainty Analysis: A Review


Cost as Probability Distribution

Monte Carlo Simulation and Method of Moments Distribution


Correlation: A Critical Consideration


Correlation Matters

Valuing Correlation


Building Statistical Cost Estimating Models


Classical Statistical Regression

General Error Regression Method


Mathematics of Cost Improvement Curves


Learning Curve Theories

Production Cost Models Built by Single-Step Regression


Enhanced Scenario-Based Method


Nonstatistical eSBM

Statistical eSBM

Historical Data for eSBM


Cost Uncertainty Analysis Practice Points

Treating Cost as a Random Variable

Risk versus Uncertainty

Subjective Probability Assessments

Subjectivity in Systems Engineering and Analysis Problems


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


Journal Publications

Conference Presentations and Proceedings



Exercises and References appear at the end of each chapter.

About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
TECHNOLOGY & ENGINEERING / Engineering (General)