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 Connecticut Reserve Technologies, Inc

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 2Computing Reliability The General Case Conventional Monte Carlo Method Basic Variables and the Limit State Function Reliability Index  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

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

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 Introduction Nonparametric Boot Strap Methods Section 7Other Features “Transient” Reliability Appendix AStatistics Fundamentals “Transient” Reliability