Mechanical Reliability Improvement: Probability and Statistics for Experimental Testing

by Little; Robert

• ISBN13: 9780824708122
• ISBN10: 0824708121
• eBook ISBN(s): 9781135563448
• Edition: CD
• Format: Hardcover
• Copyright: 2002-09-25
• Publisher: CRC Press
• More Book Details

Summary

Providing probability and statistical concepts developed using pseudorandom numbers, this book covers enumeration-, simulation-, and randomization-based statistical analyses for comparison of the test performance of alternative designs, as well as simulation- and randomization-based tests for examination of the credibility of statistical presumptions. the book discusses centroid and moment of inertia analogies for mean and variance and the organization structure of completely randomized, randomized complete block, and split spot experiment test programs. Purchase of the text provides access to 200 microcomputer programs illustrating a wide range of reliability and statistical analyses.

Author Biography

R. E. Little is Professor of Mechanical Engineering, The University of Michigan-Dearborn.

Table of Contents

Preface	v
Introduction	ix
Experiment Test Program Planning and Statistical Analysis Fundamentals	1	(28)
Introduction	1	(1)
Test Objective	1	(2)
Experiment Test Program Planning Fundamentals	3	(12)
Experiment Test Program Planning Tips	15	(1)
Statistical Analysis Fundamentals	16	(8)
Closure	24	(5)
Supplemental Topic: Planned Experiment Test Program Statistical Terminology	25	(4)
Planned Experiment Test Programs with Orthogonal Conceptual Statistical Models	29	(55)
Introduction	29	(1)
Completely Randomized Design Experiment Test Programs	29	(28)
Unreplicated Randomized Complete Block Design Experiment Test Programs	57	(6)
Unreplicated Split-Plot Design Experiment Test Programs	63	(10)
Mechanical Reliability Applications of Statistically Planned Experiment Test Programs	73	(2)
Closure	75	(9)
Supplemental Topic: Choosing Physically Relevant Conceptual Treatment Effect Contrasts	76	(3)
Supplemental Topic: Fractional Factorial Arrangements and Statistical Confounding	79	(5)
Basic Probability and Statistics Concepts and Their Mechanical Reliability Applications	84	(67)
Introduction	84	(1)
Exact Enumeration-Based Probability	84	(13)
Empirical Simulation-Based Probability	97	(1)
Empirical Randomization-Based Probability	98	(3)
Simulation-Based Demonstrations of Fundamental Probability Behaviors	101	(16)
Conceptual Statistical Distribution that Consists of All Possible Replicate Realization Values for a Generic Random Variable X with a Continuous Metric	117	(1)
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	118	(4)
Sampling Distributions	122	(3)
Technical Definition for the Null Hypothesis that B=A Statistically and for the Simple (One-Sided) Alternative Hypothesis that B > A Statistically	125	(2)
Mechanical Reliability Perspective	127	(1)
Closure	128	(23)
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	129	(3)
Supplemental Topic: Conceptual (One-Parameter) Binomial Distribution	132	(9)
Supplemental Topic: Lower 100(SCP)% (One-Sided) Statistical Confidence Limits	141	(3)
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	144	(7)
The Classical Statistical Presumption of Normally Distributed Experiment Test Program Datum Values	151	(25)
Introduction	151	(1)
Conceptual Sampling Distribution that Consists of All Possible Replicate Realization Values for the Statistic (the Sum of ns Uniform Pseudorandom Numbers)	151	(10)
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 ns Pseudorandom Numbers)	161	(7)
Closure	168	(8)
Supplemental Topic: Randomization-Based Test of the Null Hypothesis of Independence for Paired Datum Values Versus the Alternative Hypothesis of a Monotonic Association	168	(8)
The Conceptual (Two-Parameter) Normal Distribution and the Associated Conceptual Sampling Distributions for Pearson's Central Χ2 (Chi Square), Snedecor's Central F, and Student's Central t Test Statistics	176	(55)
Conceptual (Two-Parameter) Normal Distribution	176	(7)
Plotting Replicate Datum Values on Probability Paper	183	(1)
Simulation Study of Normally Distributed Pseudorandom Datum Values Plotted on Normal Probability Paper	184	(9)
Estimating Mean (X) and STDDEV (X) Given Replicate Datum Values Randomly Selected from a Conceptual (Two-Parameter) Normal Distribution	193	(2)
Testing Normality for Replicate Datum Values	195	(6)
Conceptual Sampling Distributions for Statistics Based on Datum Values Randomly Selected from a Conceptual (Two-Parameter) Normal Distribution	201	(8)
Classical (Shortest) 100 (SCP)% (Two-Sided) Statistical Confidence Interval that Allegedly Includes Mean(X)-Computed Using Student's Central t Conceptual Sampling Distribution	209	(13)
Same Classical Shortest 100(SCP)% (Two-Sided) Statistical Confidence Interval that Allegedly Includes Mean (X)-Computed Using Snedecor's Central F Conceptual Sampling Distribution	222	(2)
Classical 100(SCP)% (Two-Sided) Statistical Confidence Interval that Allegedly Includes Var(X)-Computed Using Pearson's Central x2 Conceptual Sampling Distribution	224	(2)
Closure	226	(5)
Supplemental Topic: Statistical Estimators	226	(5)
Statistical Analysis of Variance (ANOVA)	231	(77)
Classical Statistical Analysis of Variance (Fixed Effects Model)	231	(1)
A Demonstration of Validity of Snedecor's Central F Test Statistic in ANOVA Using Four Constructed Data Sets	232	(13)
Classical ANOVA Using Snedecor's Central F Test Statistic	245	(31)
Comparing All Pairs of Conceptual Treatment Means	276	(2)
Checking the Presumptions Underlying Classical ANOVA	278	(6)
Statistical Power	284	(4)
Enumeration-Based and Randomization-Based ANOVA's	288	(9)
Closure	297	(11)
Supplemental Topic: Exact Statistical Power Calculation Example	297	(5)
Supplemental Topic: The Concept of a Weighted Average	302	(3)
Supplemental Topic: Testing for Batch-to-Batch Effects	305	(3)
Linear Regression Analysis	308	(79)
Introduction	308	(3)
Simple Linear Regression Analysis	311	(41)
Multiple Linear Regression Analysis	352	(4)
Balancing Spurious Effects of Nuisance Variables in Linear Regression Experiment Test Programs	356	(1)
Closure	357	(30)
Supplemental Topic: Propagation of Variability	358	(16)
Supplemental Topic: Weighted Simple Linear Regression Analysis	374	(10)
Supplemental Topic: Classical Hyperbolic 100(SCP)% (Two-Sided) Statistical Confidence Bands in Simple Linear Regression	384	(3)
Mechanical Reliability Fundamentals and Example Analyses	387	(194)
Introduction	387	(1)
Mechanical Reliability Terminology	388	(1)
Conceptual Statistical Model for Fatigue Failure and Associated Life (Endurance) and Strength (Resistance) Experiment Test Programs	389	(2)
Life (Endurance) Experiment Test Programs	391	(4)
Strength (Resistance) Experiment Test Programs	395	(8)
Conceptual Statistical Distributions for Modeling Outcomes of Life (Endurance) and Strength (Resistance) Experiment Test Programs	403	(1)
Conceptual Life (Endurance) Distributions	403	(2)
Conceptual Life (Endurance) Distributions with a Concomitant Independent Variable	405	(1)
Conceptual Strength (Resistance) Distributions	406	(3)
Quantitative Analyses for the Outcomes of Life (Endurance) and Strength (Resistance) Experiment Test Programs	409	(1)
Quantitative Maximum Likelihood Analysis	410	(2)
Quantitative Maximum Likelihood Examples	412	(31)
Comparative Analyses for Outcomes of a Life (Endurance) and Strength (Resistance) Experiment Test Programs	443	(1)
Comparative Maximum Likelihood Analyses	443	(6)
Comparative Analysis for Outcomes of a Life (Endurance) Experiment Test Program, Based on a Generalized Savage Distribution-Free (Non-Parametric) Test Statistic	449	(2)
Estimating Sub System Reliability	451	(8)
Closure	459	(122)
Supplemental Topic: Exact (Unbiased) A-Basis and B-Basis Statistical Tolerance Limits Based on Uncensored Replicate Datum Values	460	(16)
Supplemental Topic: Maximum Likelihood Analysis for Outcome of a Life (Endurance) Experiment Test Program with Type-I Censoring, Presuming loge Normal Datum Values	476	(3)
Supplemental Topic: Maximum Likelihood Analysis for Outcome of a Strength (Resistance) Experiment Test Program with Two or More Stress (Stimulus) Levels	479	(22)
Supplemental Topic: Generating Pseudorandom Datum Values and Computing Pragmatic Statistical Bias Corrections for ML-Based Estimates	501	(39)
Supplemental Topic: Classical and Likelihood Ratio Lower 100(SCP)% (One-Sided) Asymptotic Statistical Confidence Bands and Limits	540	(19)
Supplemental Topic: Testing Statistical Adequacy of Presumed Conceptual Model Using the LR Method	559	(22)
Index	581