Design Decisions under Uncertainty with Limited Information: Structures and Infrastructures Book Series, Vol. 7(Structures and Infrastructures)

Reliability methods are becoming increasingly popular in engineering design because they help build safer and more efficient products than traditional deterministic methods. A principal challenge in using these methods in practical design problems is to model uncertainty when little data is available and the underlying mechanism of uncertain events is unknown. There is a need for an integrated presentation of tools for modeling uncertainty and making design decisions under severe uncertainty, which bridges the gap between theory and practice for methods for design under uncertainty. This work presents and compares the most important theories for modeling uncertainty and explains what tools are most suitable for a given design problem. It illustrates how to solve practical design problems in the aerospace and automotive engineering industries with a balanced approach explaining both the theoretical foundations of methods and their application to engineering design. The numerous examples in each section will help to appreciate the importance of design under uncertainty and the theoretical developments of the methods. Readers will learn a structured, risk-based approach for design under uncertainty when limited information is available, which tools are available and which to select and apply given a design decision problem. They will further understand how to improve their overall performance using a structured, risk-based approach for design under uncertainty. Intended for mechanical and civil engineers working in aerospace, automotive, civil, shipbuilding and power engineering, and for graduate level courses and students in reliability analysis and design and decision-making under uncertainty.

Table of Contents:

1. Design Decision under Uncertainty
1.1 Decision under Uncertainty
1.1.1 Good versus bad decisions
1.1.2 Elements of a Decision
1.1.3 Limited Information
1.2 The Role of Decision Analysis in Engineering Design
1.2.1 Sequential decisions in product development
1.2.2 Challenges in design decision making under uncertainty and scope of this book
1.3 Outline of this Book
1.4 Conclusion
Questions
References

2. Overview of Theories of Uncertainty and Tools for Modeling Uncertainty
2.1 Introduction: Management of Uncertainty in Design
2.2 Theories of Uncertainty
2.2.1 Intervals
2.2.2 Convex Sets
2.2.3 Objective Probability
2.2.4 Subjective Probability
2.2.5 Imprecise Probability
2.2.6 Dempster-Shafer Evidence Theory
2.3 Conclusion
References

3. Objective Probability
Overview of this chapter
3.1 Probability and Random Variables for Modeling Uncertainty
3.1.1 Fundamentals of Objective Probability
3.1.1.1 Definition of probability
3.1.1.2 Axioms of probability
3.1.1.3 Conditional probability
3.1.1.4 Combined experiments
Questions and Exercises
3.1.2 Random variables
3.1.2.1 Discrete random variables
3.1.2.2 Continuous random variables
3.1.2.3 Conditional Probability Distribution and Density Functions
Questions and exercises
3.1.3 Multiple random variables
3.1.3.1 Discrete random variables
3.1.3.2 Continuous random variables
Questions and exercises
3.2 Common probabilistic models
3.2.1 Distributions of a single random variable
3.2.1.1 Discrete variables
3.2.1.2 Continuous variables
3.2.2 Joint normal distribution
Summary of section 3.2
Questions and Exercises
3.3 Probability calculations
3.3.1 Probability distributions of a function of one random variable
3.3.1.1 Probability distribution
3.3.1.2 Probability density function
3.3.1.3 Mean value and standard deviation of a function of one variable
3.3.2 Distribution of functions of multiple random variables
3.3.1.1 One function of two variables
3.3.2.2 Two functions of two random variables
3.3.2.3 The method of auxiliary variables
3.3.2.4 Mean value and standard deviation of a function of many variables
3.3.2.5 Calculations involving normal random variables
Questions and Exercises
3.4 Concluding Remarks
References
Appendix

4. Statistical Inference – Constructing Probabilistic Models from Observations
4.1 Introduction
4.1.1 Objective, scope and summary of this chapter
4.2 Estimating mean values of random variables and probabilities of events
4.2.1 Sample mean
4.2.2 Sample variance
4.2.3 Covariance and Correlation
4.2.5 Confidence Interval for Variance
4.2.6 Probability of an Event
4.2.7 How to get the maximum return from your budget for data collection
4.3 Statistical hypothesis testing
4.4 Selecting input probability distributions
4.4.1 Step 1: Select families of probability distributions
4.4.2 Step 2: Estimate the distribution parameters
4.4.3 Step 3: Assess fit of selected distributions to observed data
4.5 Modeling dependent variables
4.5.1 Overview of methods for modeling dependence
4.5.2 Copulas for modeling dependence
4.6 Conclusion
References

5. Probabilistic Analysis of Dynamic Systems

6. Subjective (Bayesian) Probability
6.1 Definition of Subjective Probability
6.1.1 Overview
6.1.2 Axiomatic definition of probability
6.1.3 Conditional probability
6.1.4 Principle of insufficient reason
Questions and problems
6.2 Eliciting Expert’s Judgments in Order to Construct Models of Uncertaint
6.2.1 Elicitation process
6.2.2 Eliciting probabilities
6.2.3 Estimation of probabilities of rare events
6.2.4 Eliciting probability distributions
6.2.5 Representing uncertainty about an elicited distribution by a second-order probabilistic model
Questions and Problems
6.3 Bayesian Analysis
6.3.1 Motivation
6.3.2 How to update a probability distribution using observations or expert judgment
6.3.3 Accounting for imprecision by using probability bounds
Questions and Problems
6.4 Heuristics and biases in probability judgments
Questions
6.5 Concluding remarks
References

7. Decision Analysis
7.1 Introduction
7.1.1 Examples of Decision Problems
7.1.2 Elements of Decision Problems and Terminology
7.1.4 Steps of the Decision Process
7.1.5 Outline of this chapter
Questions and Problems
7.2 Framing and Structuring Decisions
7.2.1 Define and frame a decision
7.2.2 Structure a Decision Problem
Questions and problems
7.3 Solving Decision Problems
7.3.1 Backward induction (or folding back the decision tree)
Exercises and problems
7.4 Performing Sensitivity Analysis
7.4.1 Introduction
7.4.2 Sensitivity to the definition, framing and structure of the problem
7.4.3 One-way sensitivity analysis
7.4.4 Two-way sensitivity analysis
7.4.5 Sensitivity of the selection of the optimum option to imprecision in probabilities
Questions and problems
7.5 Modeling Preferences
7.5.1 Motivation
7.5.2 Simple criteria for decision making
7.5.3 Utility
7.5.4 Axioms of utility
Questions and problems
7.6 Conclusion
References

8. Multiattribute Considerations in Design
8.1 Tradeoff between attributes
8.1.1 Range of negotiability
8.1.2 Value functions vs. Utility functions
Question and Problems:
8.2 Different multiattribute formulations
8.2.1 Single-Attribute based formulations
8.2.1.1 Independence conditions
8.2.1.2 The additive form of multiattribute utility function
8.2.1.3 The multi-linear form of multiattribute utility function
8.2.2 Assessing the scaling constants
8.2.3 Value function based formulation
8.2.4 Attribute dominance utility and multiattribute utility copulas
8.3 Solving decision problems under uncertainty using multiattribute utility analysis
8.4 Conclusions
Questions and Problems
References