A Short Course on:Weibull Analysis & Parameter Estimation for

Ceramic Reliability

Presented at:Honeywell

March 14 – 17, 2006Stephen F. Duffy PhD, PE

Connecticut Reserve Technologies, IncCleveland State University

Eric H. BakerConnecticut Reserve Technologies, Inc

Table of Contents

Section 1 Load & Resistance (Fundamentals)Structural Reliability: FundamentalsLoad/Resistance Analysis: An Approximate Approach (J. Margetson)Reliability AnalysisProof Testing: Truncated Distributions

Section 2 Computing ReliabilityThe General CaseConventional Monte Carlo MethodBasic Variables and the Limit State FunctionReliability Index Interpreting the Reliability Index

Section 3 System Reliability & Weibull AnalysisSystem Reliability - Series SystemExample – Truss Problem (overheads)Two Parameter Weibull Distribution with Size EffectsComponent ReliabilityMultiaxial Reliability ModelsPIA – A Phenomenological ModelWeibull Analysis – Closed Form Examples (overheads)Batdorf’s Theory - Mechanistic ModelCARES - Fast Fracture ExamplesProof Testing & the Weibull Distribution

Table of Contents (continued)

Section 4 Parameter Estimation for Fast Fracture Strength DataIntroduction to Estimation TheoryPoint Estimation: PreliminariesMethod of Moments (overheads)Minimizing ResidualsProbabilistic Regression AnalysisLinear Regression – Two Parameter Weibull DistributionProbability of Failure: Ranking SchemesMethod of Maximum Likelihood (MLE)MLE: Two Parameter Weibull DistributionExample - Single Flaw DistributionParameter Estimate BiasConfidence Bounds on Parameter EstimatesMultiple Flaw PopulationsMLEs For Multiple Flaw DistributionsExample – Multiple Flaw DistributionsNon-Linear Regression Analysis: Three Parameter Weibull DistributionExample – Three Parameter Weibull DistributionIsothermal Pooled Data

Table of Contents (continued)

Section 5 Time Dependent Weibull AnalysisIntroductionSubcritical Crack Growth ModelTime Dependent Batdorf ModelTime Dependent PIA ModelSubcritical 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 ReliabilityIntroductionNonparametric Boot Strap Methods

Section 7 Other Features“Transient” Reliability

Appendix A Statistics Fundamentals“Transient” Reliability