Probability Methods for Cost Uncertainty Analysis
A Systems Engineering Perspective, Second Edition
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
Sample Spaces and Events
Interpretations and Axioms of Probability
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
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
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
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
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
Collected Works of Dr. Stephen A. Book
Conference Presentations and Proceedings
Exercises and References appear at the end of each chapter.
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.
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