Probability Methods for Cost Uncertainty Analysis: A Systems Engineering Perspective, Second Edition

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



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.

Features

• Presents recently developed methods for cost uncertainty analysis, including the general error regression method (GERM) and enhanced scenario-based method (eSBM)
• Shows how to incorporate the effect of correlation on measures of cost risk
• Explains how to present and interpret cost as a probability distribution
• Provides recommended practices and lessons when performing cost uncertainty analyses
• Includes many examples that highlight the application of mathematical concepts to real-world systems engineering and cost risk analysis problems
• Contains a set of theoretical and applied exercises at the end of each chapter

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