This graduate textbook imparts the fundamentals of reliability and risk that can be connected mathematically and applied to problems in engineering and medical science and practice. The book is divided into eight chapters, the first three of which deal with basic fundamentals of probability theory and reliability methods. The fourth chapter illustrates simulation methods needed to solve complex problems. Chapters 5-7 explain reliability codes and system reliability (which uses the component reliabilities discussed in previous chapters). The book concludes in chapter 8 with an examination of applications of reliability within engineering and medical fields. Presenting a highly relevant competency for graduates entering product research and development, or facilities operations sectors, this text includes many examples and end of chapter study questions to maximize student comprehension.
- Explains concepts of reliability and risk estimation techniques in the context of medicine and engineering;
- Elucidates the interplay between reliability and risk from design to operation phases;
- Uses real world examples from engineering structures and medical devices and protocols;
- Adopts a lucid yet rigorous presentation of reliability and risk calculations;
- Reinforces students understanding of concepts covered with end-of-chapter exercises.
Author(s): Chandrasekhar Putcha, Subhrajit Dutta, Sanjay K. Gupta
Series: Transactions on Computational Science and Computational Intelligence
Publisher: Springer
Year: 2021
Language: English
Pages: 141
City: Cham
Preface
Contents
About the Authors
Chapter 1: Probability and Density Functions
1.1 Introduction
1.1.1 Data Analysis
1.2 Most Important Distributions Used in Practice Are Given Below
1.2.1 Normal Distribution Function
1.2.1.1 Parameters
1.2.2 Lognormal Distribution
1.2.2.1 Parameters
1.2.3 Uniform Distribution
1.2.3.1 Parameters
1.2.4 Exponential Distribution
1.2.4.1 Parameters
1.2.5 Weibull Distribution
1.2.5.1 Parameters
1.2.6 Beta Distribution
1.2.6.1 Parameters
1.2.7 Gamma Distribution
1.2.7.1 Parameters (υ, k)
1.3 Examples
References
Chapter 2: Reliability and Risk Analysis
2.1 Introductory Remarks
2.2 Definitions of Reliability and Risk
2.2.1 Definition of Risk
2.2.2 Definition of Reliability
2.3 Mathematical Definition of Risk
2.4 Reliability Examples
2.5 Additional Definitions of Risk
References
Chapter 3: System Reliability
3.1 Series Systems
3.2 Parallel Systems
3.3 Series - Parallel Systems
3.4 Mixed System
3.5 Practical Applications
3.6 High Level Redundancy and Low Level Redundancy
3.6.1 Low-Level Redundancy
3.6.2 High-Level Redundancy
3.7 Generic Applications of RBD
3.8 Engineering Applications of RBD
References
Chapter 4: Regression Analysis
4.1 Introduction
4.2 Regression Models
4.2.1 Generalized Procedure for Regression Model Construction
4.2.2 Regression Model Testing
4.2.3 Types of Regression Models
4.2.3.1 Polynomial Regression Models
The Polynomial Regression Model
Least Square Error Minimization for Parameter Estimation
Accuracy of the Polynomial Regression Model
4.2.3.2 Support Vector Regression
4.3 Gaussian Process Regression Model
4.3.1 Prediction with Gaussian Processes
4.3.2 Determination of Kriging Hyper-Parameters
4.4 Basic Theory and Examples of Regression Analysis
4.4.1 Linear Regression
4.4.2 Polynomial Regression
4.4.3 Equivalent Linear Regression
4.5 Concluding Remarks
References
Chapter 5: Probabilistic Simulation Methods
5.1 Introduction
5.2 Probabilistic Simulation Methods
5.2.1 Monte Carlo Simulation
5.2.2 Simplistic Approach to Monte Carlo Simulation
5.3 Basic Procedure for Monte Carlo Simulation
5.4 Quasi Monte Carlo Samling
5.4.1 Latin Hypercube Sampling
5.5 Importance Sampling
5.6 Examples
5.6.1 Analytical Problems: Ishigami Function
5.7 Numerical Problem: Finite Element Models
5.7.1 Truss Structure
5.7.2 Tensile Membrane Structure
Reference
Chapter 6: Decision Theory
6.1 Introduction
6.2 Flow Chart
6.3 Decision Tree
6.4 Problems Related to Decision Trees
6.5 Entropy in Decision Trees
6.6 Mathematical Definition of Entropy
6.7 Limits of Decision Trees
References
Chapter 7: Medical Applications I
7.1 Introduction
7.2 Stroke Index
7.3 Concept of Resistance and Load Model in the Context of Medical Data
7.4 Example Problems in Medical Area
References
Chapter 8: Medical Applications II
8.1 Post Traumatic Stress Syndrome
8.2 Factors Influencing Post Traumatic Stress
8.3 Post Traumatic Stress Index (PTSI)
8.4 PTS Index for Population of Alabama (Sample Calculation)
8.5 Effect of Clinical/Physician Intervention
8.6 Post Treatment PTSI: General Population of Alabama
8.7 Impact of the PTS Index: Regression Analysis
8.8 Concluding Remarks
References
Index
