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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 | |