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| Preface | |
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| Introduction | |
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| Experiment Test Program Planning and Statistical Analysis Fundamentals | |
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| Introduction | |
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| Test Objective | |
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| Experiment Test Program Planning Fundamentals | |
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| Experiment Test Program Planning Tips | |
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| Statistical Analysis Fundamentals | |
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| Closure | |
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| Supplemental Topic: Planned Experiment Test Program Statistical Terminology | |
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| Planned Experiment Test Programs with Orthogonal Conceptual Statistical Models | |
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| Introduction | |
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| Completely Randomized Design Experiment Test Programs | |
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| Unreplicated Randomized Complete Block Design Experiment Test Programs | |
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| Unreplicated Split-Plot Design Experiment Test Programs | |
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| Mechanical Reliability Applications of Statistically Planned Experiment Test Programs | |
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| Closure | |
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| Supplemental Topic: Choosing Physically Relevant Conceptual Treatment Effect Contrasts | |
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| Supplemental Topic: Fractional Factorial Arrangements and Statistical Confounding | |
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| Basic Probability and Statistics Concepts and Their Mechanical Reliability Applications | |
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| Introduction | |
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| Exact Enumeration-Based Probability | |
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| Empirical Simulation-Based Probability | |
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| Empirical Randomization-Based Probability | |
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| Simulation-Based Demonstrations of Fundamental Probability Behaviors | |
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| Conceptual Statistical Distribution that Consists of All Possible Replicate Realization Values for a Generic Random Variable X with a Continuous Metric | |
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| Actual Values for the Mean and Variance of the Conceptual Statistical Distribution that Consists of all Possible Replicate Realization Values for a Generic Random Variable X with a Continuous Metric | |
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| Sampling Distributions | |
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| Technical Definition for the Null Hypothesis that B = A Statistically and for the Simple (One-Sided) Alternative Hypothesis that B > A Statistically | |
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| Mechanical Reliability Perspective | |
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| Closure | |
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| Supplemental Topic: Statistical Weights of Datum Values and Actual Values for the Mean and Variance of the Conceptual Statistical Distribution that Consists of All Possible Replicate Realization Values for a Random Variable with a Discrete Metric | |
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| Supplemental Topic: Conceptual (One-Parameter) Binomial Distribution | |
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| Supplemental Topic: Lower 100(SCP)% (One-Sided) Statistical Confidence Limits | |
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| Supplemental Topic: Randomization-Based Test of the Null Hypothesis that B = A Statistically Versus the Simple (One-Sided) Alternative Hypothesis that B > A Statistically Pertaining to a CRD Experiment Test Program | |
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| The Classical Statistical Presumption of Normally Distributed Experiment Test Program Datum Values | |
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| Introduction | |
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| Conceptual Sampling Distribution that Consists of All Possible Replicate Realization Values for the Statistic (the Sum of n[subscript s] Uniform Pseudorandom Numbers) | |
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| Accuracy of the Conceptual (Two-Parameter) Normal Distribution Approximation to the Conceptual Sampling Distribution that Consists of All Possible Replicate Realization Values for the Statistic (the Sum of n[subscript s] Pseudorandom Numbers) | |
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| Closure | |
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| Supplemental Topic: Randomization-Based Test of the Null Hypothesis of Independence for Paired Datum Values Versus the Alternative Hypothesis of a Monotonic Association | |
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| The Conceptual (Two-Parameter) Normal Distribution and the Associated Conceptual Sampling Distributions for Pearson's Central x[superscript 2] (Chi Square), Snedecor's Central F, and Student's Central t Test Statistics | |
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| Conceptual (Two-Parameter) Normal Distribution | |
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| Plotting Replicate Datum Values on Probability Paper | |
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| Simulation Study of Normally Distributed Pseudorandom Datum Values Plotted on Normal Probability Paper | |
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| Estimating Mean(X) and STDDEV(X) Given Replicate Datum Values Randomly Selected from a Conceptual (Two-Parameter) Normal Distribution | |
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| Testing Normality for Replicate Datum Values | |
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| Conceptual Sampling Distributions for Statistics Based on Datum Values Randomly Selected from a Conceptual (Two-Parameter) Normal Distribution | |
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| Classical (Shortest) 100(SCP)% (Two-Sided) Statistical Confidence Interval that Allegedly Includes Mean(X)-Computed Using Student's Central t Conceptual Sampling Distribution | |
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| Same Classical Shortest 100(SCP)% (Two-Sided) Statistical Confidence Interval that Allegedly Includes Mean(X)-Computed Using Snedecor's Central F Conceptual Sampling Distribution | |
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| Classical 100(SCP)% (Two-Sided) Statistical Confidence Interval that Allegedly Includes Var(X)-Computed Using Pearson's Central x[superscript 2] Conceptual Sampling Distribution | |
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| Closure | |
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| Supplemental Topic: Statistical Estimators | |
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| Statistical Analysis of Variance (ANOVA) | |
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| Classical Statistical Analysis of Variance (Fixed Effects Model) | |
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| A Demonstration of Validity of Snedecor's Central F Test Statistic in ANOVA Using Four Constructed Data Sets | |
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| Classical ANOVA Using Snedecor's Central F Test Statistic | |
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| Comparing All Pairs of Conceptual Treatment Means | |
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| Checking the Presumptions Underlying Classical ANOVA | |
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| Statistical Power | |
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| Enumeration-Based and Randomization-Based ANOVA's | |
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| Closure | |
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| Supplemental Topic: Exact Statistical Power Calculation Example | |
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| Supplemental Topic: The Concept of a Weighted Average | |
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| Supplemental Topic: Testing for Batch-to-Batch Effects | |
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| Linear Regression Analysis | |
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| Introduction | |
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| Simple Linear Regression Analysis | |
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| Multiple Linear Regression Analysis | |
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| Balancing Spurious Effects of Nuisance Variables in Linear Regression Experiment Test Programs | |
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| Closure | |
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| Supplemental Topic: Propagation of Variability | |
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| Supplemental Topic: Weighted Simple Linear Regression Analysis | |
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| Supplemental Topic: Classical Hyperbolic 100(SCP)% (Two-Sided) Statistical Confidence Bands in Simple Linear Regression | |
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| Mechanical Reliability Fundamentals and Example Analyses | |
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| Introduction | |
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| Mechanical Reliability Terminology | |
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| Conceptual Statistical Model for Fatigue Failure and Associated Life (Endurance) and Strength (Resistance) Experiment Test Programs | |
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| Life (Endurance) Experiment Test Programs | |
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| Strength (Resistance) Experiment Test Programs | |
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| Conceptual Statistical Distributions for Modeling Outcomes of Life (Endurance) and Strength (Resistance) Experiment Test Programs | |
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| Conceptual Life (Endurance) Distributions | |
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| Conceptual Life (Endurance) Distributions with a Concomitant Independent Variable | |
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| Conceptual Strength (Resistance) Distributions | |
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| Quantitative Analyses for the Outcomes of Life (Endurance) and Strength (Resistance) Experiment Test Programs | |
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| Quantitative Maximum Likelihood Analysis | |
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| Quantitative Maximum Likelihood Examples | |
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| Comparative Analyses for Outcomes of Life (Endurance) and Strength (Resistance) Experiment Test Programs | |
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| Comparative Maximum Likelihood Analyses | |
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| Comparative Analysis for Outcome of a Life (Endurance) Experiment Test Program, Based on a Generalized Savage Distribution-Free (Non-Parametric) Test Statistic | |
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| Estimating Sub System Reliability | |
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| Closure | |
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| Supplemental Topic: Exact (Unbiased) A-Basis and B-Basis Statistical Tolerance Limits Based on Uncensored Replicate Datum Values | |
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| Supplemental Topic: Maximum Likelihood Analysis for Outcome of a Life (Endurance) Experiment Test Program with Type-I Censoring, Presuming log[subscript e] Normal Datum Values | |
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| Supplemental Topic: Maximum Likelihood Analysis for Outcome of a Strength (Resistance) Experiment Test Program with Two or More Stress (Stimulus) Levels | |
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| Supplemental Topic: Generating Pseudorandom Datum Values and Computing Pragmatic Statistical Bias Corrections for ML-Based Estimates | |
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| Supplemental Topic: Classical and Likelihood Ratio Lower 100(SCP)% (One-Sided) Asymptotic Statistical Confidence Bands and Limits | |
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| Supplemental Topic: Testing Statistical Adequacy of Presumed Conceptual Model Using the LR Method | |
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| Index | |