1. Weibull Analysis & Parameter Estimation for Ceramic Reliability
A Short Course on:
Weibull Analysis & Parameter Estimation for Ceramic Reliability
Presented at:
Honeywell
March 14 – 17, 2006
Stephen F. Duffy PhD, PE
Connecticut Reserve Technologies, Inc
Cleveland State University
Eric H. Baker

2. Table of Contents
Section 1 Load & Resistance (Fundamentals)
Structural Reliability: Fundamentals
Load/Resistance Analysis: An Approximate Approach (J. Margetson)
Reliability Analysis
Proof Testing: Truncated Distributions
Section 2 Computing Reliability
The General Case
Conventional Monte Carlo Method
Basic Variables and the Limit State Function
Reliability Index b
Interpreting the Reliability Index
Section 3 System Reliability & Weibull Analysis
System Reliability - Series System
Example – Truss Problem (overheads)
Two Parameter Weibull Distribution with Size Effects
Component Reliability
Multiaxial Reliability Models
PIA – A Phenomenological Model
Weibull Analysis – Closed Form Examples (overheads)
Batdorf’s Theory - Mechanistic Model
CARES - Fast Fracture Examples
Proof Testing & the Weibull Distribution

3. Table of Contents (continued)
Section 4 Parameter Estimation for Fast Fracture Strength Data
Introduction to Estimation Theory
Point Estimation: Preliminaries
Method of Moments (overheads)
Minimizing Residuals
Probabilistic Regression Analysis
Linear Regression – Two Parameter Weibull Distribution
Probability of Failure: Ranking Schemes
Method of Maximum Likelihood (MLE)
MLE: Two Parameter Weibull Distribution
Example - Single Flaw Distribution
Parameter Estimate Bias
Confidence Bounds on Parameter Estimates
Multiple Flaw Populations
MLEs For Multiple Flaw Distributions
Example – Multiple Flaw Distributions
Non-Linear Regression Analysis: Three Parameter Weibull Distribution
Example – Three Parameter Weibull Distribution
Isothermal Pooled Data

4. Table of Contents (continued)
Section 5 Time Dependent Weibull Analysis
Introduction
Subcritical Crack Growth Model
Time Dependent Batdorf Model
Time Dependent PIA Model
Subcritical Crack Growth Model: Creep (Static Fatigue)
Subcritical Crack Growth Model: Monotonic Loading (Dynamic Fatigue)
Parameter Estimation: Time Dependent Strength Data
Section 6 Confidence Bounds on Component Reliability
Nonparametric Boot Strap Methods
Section 7 Other Features
“Transient” Reliability
Appendix A Statistics Fundamentals