A Short Course on: Weibull Analysis & Parameter

A Short Course on: Weibull Analysis & Parameter

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 2

Computing 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) Batdorfs 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 7 Other Features Transient Reliability

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