book

Practical Applications of Bayesian Reliability

by Yan Liu, Athula I. Abeyratne

May 2019

Intermediate to advanced

320 pages

9h 17m

English

Wiley

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1.1 Introduction1.2 Basic Theory and Concepts of Reliability Statistics1.3 Bayesian Approach to Reliability Inferences1.4 Component Reliability Estimation1.5 System Reliability Estimation1.6 Design Capability Prediction (Monte Carlo Simulations)1.7 SummaryReferences
2.1 Basic Idea of Bayesian Reasoning2.2 Basic Probability Theory and Bayes' Theorem2.3 Bayesian Inference (Point and Interval Estimation)2.4 Selection of Prior Distributions2.5 Bayesian Inference vs. Frequentist Inference2.6 How Bayesian Inference Works with Monte Carlo Simulations2.7 Bayes Factor and its Applications2.8 Predictive Distribution2.9 SummaryReferences
3.1 Introduction3.2 Discretization3.3 Markov Chain Monte Carlo Algorithms3.4 Using BUGS/JAGS3.5 SummaryReferences
4.1 Introduction4.2 Discrete Probability Models4.3 Continuous Models4.4 Model and Convergence DiagnosticsReferences
5.1 Classical Zero‐failure Test Plans for Substantiation Testing5.2 Classical Zero‐failure Test Plans for Reliability Testing5.3 Bayesian Zero‐failure Test Plan for Substantiation Testing5.4 Bayesian Zero‐failure Test Plan for Reliability Testing5.5 SummaryReferences
6.1 Introduction6.2 Monte Caro Simulations with Parameter Point Estimates6.3 Nested Monte Carlo Simulations with Bayesian Parameter Estimation6.4 SummaryReferences

7.1 Introduction7.2 Reliability Block Diagram7.3 Fault Tree7.4 Bayesian Network7.5 SummaryReferences
8.1 Introduction8.2 Bayesian Hierarchical Binomial Model8.3 Bayesian Hierarchical Weibull Model8.4 SummaryReferences
9.1 Linear Regression9.2 Binary Logistic Regression9.3 Case Study: Defibrillation Efficacy Analysis9.4 SummaryReferences
A.1 Install RA.2 Install R StudioA.3 Install JAGSA.4 Install Package rjagsA.5 Set Working Directory
B.1 How to Run R CommandsB.2 General CommandsB.3 Generate DataB.4 Variable TypesB.5 Calculations and OperationsB.6 Summarize DataB.7 Read and Write DataB.8 Plot DataB.9 Loops and Conditional Statements
Discrete DistributionsContinuous Distributions

Content preview from Practical Applications of Bayesian Reliability

Appendix AGuidance for Installing R, R Studio, JAGS, and rjags

Create a folder in a writeable directory (e.g. C:\Bayesian), and install all the programs (R, RStudio, JAGS) into this folder following the steps below.

A.1 Install R

The following are the steps to install the programming language R.

1.1 Go to website https://www.r‐project.org.
1.2 To download R, choose a CRAN mirror at webpage https://cran.r‐project.org/mirrors.html.
e.g. click the first link under category USA, which is https://cran.cnr.berkeley.edu.

This leads you to the page to download and install R.

Follow the instructions, e.g. for Windows users, select Download R for Windows.

On the following page, R for Windows, select Install R for the first time.

On the following page, select Download R x.x.x (version number) for Windows.
1.3 Run the R installation program to install R. When asked to Select Destination Location, select the folder created earlier, e.g.
C:\Bayesian\R‐3.3.0,

and follow the installation instructions.

A.2 Install R Studio

The following are the steps to install the R Studio editor, which provides a friendly graphical user interface for R programming.

2.1 Go to the R Studio website https://www.rstudio.com and select Download RStudio.
2.2 Select Download RStudio Desktop.
2.3 On the following page, select the appropriate program for your platform, e.g. RStudio x.x.xxx – Windows Vista/7/8/10.
2.4 Run the RStudio installation program to install RStudio. When asked to Choose Install Location, ...