Probability Methods for Cost Uncertainty Analysis, 2nd Edition

Probability Methods for Cost Uncertainty Analysis, 2nd Edition

by Paul R. Garvey, Stephen A. Book, Raymond P. Covert
Released January 2016
Publisher(s): Chapman and Hall/CRC
ISBN: 9781482219760

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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

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents (1/2)
  7. Table of Contents (2/2)
  8. Preface to the Second Edition
  9. Preface to the First Edition
  10. Authors
  11. Reserved Notation
  12. Section I Theory and Foundations
    1. 1. Uncertainty and the Role of Probability in Cost Analysis
      1. 1.1 Introduction and Historical Perspective
      2. 1.2 Problem Space
      3. 1.3 Presenting Cost as a Probability Distribution (1/2)
      4. 1.3 Presenting Cost as a Probability Distribution (2/2)
      5. 1.4 Benefits of Cost Uncertainty Analysis
      6. Exercises
      7. References
    2. 2. Concepts of Probability Theory
      1. 2.1 Introduction
      2. 2.2 Sample Spaces and Events
      3. 2.3 Interpretations and Axioms of Probability (1/2)
      4. 2.3 Interpretations and Axioms of Probability (2/2)
        1. 2.3.1 Equally Likely Interpretation
        2. 2.3.2 Frequency Interpretation
        3. 2.3.3 Axiomatic Definition
        4. 2.3.4 Measure of Belief Interpretation
        5. 2.3.5 Risk versus Uncertainty
      5. 2.4 Conditional Probability
      6. 2.5 Bayes’ Rule
      7. Exercises
      8. References
    3. 3. Distributions and the Theory of Expectation
      1. 3.1 Random Variables and Probability Distributions
        1. 3.1.1 Discrete Random Variables
        2. 3.1.2 Continuous Random Variables
        3. 3.1.3 Properties of FX(x)
      2. 3.2 Expectation of a Random Variable (1/3)
      3. 3.2 Expectation of a Random Variable (2/3)
      4. 3.2 Expectation of a Random Variable (3/3)
        1. 3.2.1 Expected Value of a Function
      5. 3.3 Moments of Random Variables
      6. 3.4 Probability Inequalities Useful in Cost Analysis
      7. 3.5 Cost Analysis Perspective
      8. Exercises
      9. References
    4. 4. Special Distributions for Cost Uncertainty Analysis
      1. 4.1 Trapezoidal Distribution
        1. 4.1.1 Uniform Distribution
        2. 4.1.2 Triangular Distribution
      2. 4.2 Beta Distribution
      3. 4.3 Normal Distribution (1/2)
      4. 4.3 Normal Distribution (2/2)
      5. 4.4 Lognormal Distribution (1/2)
      6. 4.4 Lognormal Distribution (2/2)
      7. 4.5 Specifying Continuous Probability Distributions (1/2)
      8. 4.5 Specifying Continuous Probability Distributions (2/2)
        1. 4.5.1 Subjective Probabilities and Distribution Functions
        2. 4.5.2 Specifying a Beta Distribution
        3. 4.5.3 Specifying Uniform Distributions
        4. 4.5.4 Specifying a Triangular Distribution
      9. Exercises
      10. References
    5. 5. Functions of Random Variables and Their Application to Cost Uncertainty Analysis
      1. 5.1 Introduction
        1. 5.1.1 Joint and Conditional Distributions
        2. 5.1.2 Independent Random Variables
        3. 5.1.3 Expectation and Correlation
      2. 5.2 Linear Combinations of Random Variables
        1. 5.2.1 Cost Considerations on Correlation
      3. 5.3 Central Limit Theorem and a Cost Perspective (1/2)
      4. 5.3 Central Limit Theorem and a Cost Perspective (2/2)
        1. 5.3.1 Further Considerations
      5. 5.4 Transformations of Random Variables (1/6)
      6. 5.4 Transformations of Random Variables (2/6)
      7. 5.4 Transformations of Random Variables (3/6)
      8. 5.4 Transformations of Random Variables (4/6)
      9. 5.4 Transformations of Random Variables (5/6)
      10. 5.4 Transformations of Random Variables (6/6)
        1. 5.4.1 Functions of a Single Random Variable
        2. 5.4.2 Applications to Software Cost-Schedule Models
        3. 5.4.3 Functions of Two Random Variables
      11. 5.5 Mellin Transform and Its Application to Cost Functions (1/4)
      12. 5.5 Mellin Transform and Its Application to Cost Functions (2/4)
      13. 5.5 Mellin Transform and Its Application to Cost Functions (3/4)
      14. 5.5 Mellin Transform and Its Application to Cost Functions (4/4)
      15. Exercises
      16. References
      17. Additional Reading
    6. 6. System Cost Uncertainty Analysis
      1. 6.1 Work Breakdown Structures
      2. 6.2 Analytical Framework (1/7)
      3. 6.2 Analytical Framework (2/7)
      4. 6.2 Analytical Framework (3/7)
      5. 6.2 Analytical Framework (4/7)
      6. 6.2 Analytical Framework (5/7)
      7. 6.2 Analytical Framework (6/7)
      8. 6.2 Analytical Framework (7/7)
        1. 6.2.1 Computing the System Cost Mean and Variance
        2. 6.2.2 Approximating the Distribution Function of System Cost
      9. 6.3 Monte Carlo Simulation (1/2)
      10. 6.3 Monte Carlo Simulation (2/2)
        1. 6.3.1 Inverse Transform Method
        2. 6.3.2 Sample Size for Monte Carlo Simulations
      11. Exercises
      12. References
    7. 7. Modeling Cost and Schedule Uncertainties: An Application of Joint Probability Theory
      1. 7.1 Introduction
      2. 7.2 Joint Probability Models for Cost-Schedule (1/4)
      3. 7.2 Joint Probability Models for Cost-Schedule (2/4)
      4. 7.2 Joint Probability Models for Cost-Schedule (3/4)
      5. 7.2 Joint Probability Models for Cost-Schedule (4/4)
        1. 7.2.1 Bivariate Normal
        2. 7.2.2 Bivariate Normal–Lognormal
        3. 7.2.3 Bivariate Lognormal
      6. 7.3 Summary
      7. Exercises
      8. References
  13. Section II Practical Considerations and Applications
    1. 8. A Review of Cost Uncertainty Analysis
      1. 8.1 Introduction
      2. 8.2 Cost as Probability Distribution
      3. 8.3 Monte Carlo Simulation and Method of Moments (1/5)
      4. 8.3 Monte Carlo Simulation and Method of Moments (2/5)
      5. 8.3 Monte Carlo Simulation and Method of Moments (3/5)
      6. 8.3 Monte Carlo Simulation and Method of Moments (4/5)
      7. 8.3 Monte Carlo Simulation and Method of Moments (5/5)
        1. 8.3.1 Monte Carlo Method
        2. 8.3.2 Method of Moments
      8. 8.4 Summary
      9. Exercises
      10. References
      11. Additional Reading
    2. 9. Correlation: A Critical Consideration
      1. 9.1 Introduction
      2. 9.2 Correlation Matters
      3. 9.3 Valuing Correlation (1/3)
      4. 9.3 Valuing Correlation (2/3)
      5. 9.3 Valuing Correlation (3/3)
        1. 9.3.1 Assigning Correlations
        2. 9.3.2 Deriving Correlations
        3. 9.3.3 Using Monte Carlo Simulation
      6. 9.4 Summary
      7. Exercises
      8. References
    3. 10. Building Statistical Cost Estimating Models
      1. 10.1 Introduction
      2. 10.2 Classical Statistical Regression (1/3)
      3. 10.2 Classical Statistical Regression (2/3)
      4. 10.2 Classical Statistical Regression (3/3)
        1. 10.2.1 Ordinary Least Squares Regression
        2. 10.2.2 Nonlinear Ordinary Least Squares Regression
      5. 10.3 General Error Regression Method (1/3)
      6. 10.3 General Error Regression Method (2/3)
      7. 10.3 General Error Regression Method (3/3)
        1. 10.3.1 Additive Error Form
        2. 10.3.2 Multiplicative Error Form
      8. 10.4 Summary
      9. Exercises
      10. References
      11. Additional Reading
    4. 11. Mathematics of Cost Improvement Curves
      1. 11.1 Introduction
      2. 11.2 Learning Curve Theories (1/3)
      3. 11.2 Learning Curve Theories (2/3)
      4. 11.2 Learning Curve Theories (3/3)
        1. 11.2.1 Similarities and Differences
        2. 11.2.2 Limitations and Considerations
        3. 11.2.3 Learning Rate Impacts on T1 Costs
        4. 11.2.4 Historically Derived Learning Rates and Cost Models
      5. 11.3 Production Cost Models Built by Single-Step Regression (1/2)
      6. 11.3 Production Cost Models Built by Single-Step Regression (2/2)
        1. 11.3.1 Quantity as an Independent Variable (QAIV)
        2. 11.3.2 Unit as an Independent Variable (UAIV)
      7. 11.4 Summary
      8. Exercises
      9. References
      10. Additional Reading
    5. 12. Enhanced Scenario-Based Method
      1. 12.1 Introduction
      2. 12.2 Nonstatistical eSBM
      3. 12.3 Statistical eSBM (1/2)
      4. 12.3 Statistical eSBM (2/2)
      5. 12.4 Historical Data for eSBM (1/2)
      6. 12.4 Historical Data for eSBM (2/2)
        1. 12.4.1 RAND Historical Cost Growth Studies
        2. 12.4.2 Naval Center for Cost Analysis: Historical Cost Growth Studies
      7. 12.5 Summary
      8. Exercises
      9. References
    6. 13. Cost Uncertainty Analysis Practice Points
      1. 13.1 Treating Cost as a Random Variable
      2. 13.2 Risk versus Uncertainty
      3. 13.3 Subjective Probability Assessments
      4. 13.4 Subjectivity in Systems Engineering and Analysis Problems
      5. 13.5 Correlation
      6. 13.6 Capturing Cost-Schedule Uncertainties
      7. 13.7 Distribution Function of a System’s Total Cost
      8. 13.8 Benefits of Cost Uncertainty Analysis
    7. 14. Collected Works of Dr. Stephen A. Book
      1. 14.1 Textbooks
      2. 14.2 Journal Publications
      3. 14.3 Conference Presentations and Proceedings
  14. Appendix A: Statistical Tables and Related Integrals (1/2)
  15. Appendix A: Statistical Tables and Related Integrals (2/2)
  16. Appendix B: Bivariate Normal-Lognormal Distribution (1/2)
  17. Appendix B: Bivariate Normal-Lognormal Distribution (2/2)
  18. Appendix C: Bivariate Lognormal Distribution (1/2)
  19. Appendix C: Bivariate Lognormal Distribution (2/2)
  20. Appendix D: Method of Moments WBS Example
  21. Appendix E: Unraveling the S-Curve (1/2)
  22. Appendix E: Unraveling the S-Curve (2/2)
  23. Appendix F: Iteratively Reweighted Least Squares (1/2)
  24. Appendix F: Iteratively Reweighted Least Squares (2/2)
  25. Appendix G: Sample Lot Cost and Quantity Data
  26. Index (1/3)
  27. Index (2/3)
  28. Index (3/3)

Product information

  • Title: Probability Methods for Cost Uncertainty Analysis, 2nd Edition
  • Author(s): Paul R. Garvey, Stephen A. Book, Raymond P. Covert
  • Release date: January 2016
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781482219760