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Introduction | |

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Engineering Statistics: What and Why | |

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Basic Terminology | |

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Types of Statistical Studies | |

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Types of Data | |

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Types of Data Structures | |

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Measurement: Its Importance and Difficulty | |

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Mathematical Models, Reality, and Data Analysis | |

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Data Collection | |

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General Principles in the Collection of Engineering Data | |

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Measurement | |

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Sampling | |

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Recording | |

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Sampling in Enumerative Studies | |

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Principles for Effective Experimentation | |

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Taxonomy of Variables | |

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Handling Extraneous Variables | |

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Comparative Study | |

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Replication | |

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Allocation of Resources | |

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Some Common Experimental Plans | |

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Completely Randomized Experiments | |

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Randomized Complete Block Experiments | |

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Incomplete Block Experiments (Optional) | |

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Preparing to Collect Engineering Data | |

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A Series of Steps to Follow | |

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Problem Definition | |

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Study Definition | |

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Physical Preparation | |

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Elementary Descriptive Statistics | |

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Elementary Graphical and Tabular Treatment of Quantitative Data | |

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Dot Diagrams and Stem-and-Leaf Plots | |

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Frequency Tables and Histograms | |

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Scatterplots and Run Charts | |

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Quantiles and Related Graphical Tools | |

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Quantiles and Quantile Plots | |

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Boxplots | |

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Q-Q Plots and Comparing Distributional Shapes | |

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Standard Numerical Summary Measures | |

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Measures of Location | |

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Measures of Spread | |

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Statistics and Parameters | |

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Plots of Summary Statistics | |

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Summary Statistics and Personal Computer Software | |

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Descriptive Statistics for Qualitative and Count Data (Optional) | |

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Numerical Summarization of Qualitative and Count Data | |

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Bar Charts and Plots for Qualitative and Count Data | |

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Describing Relationships Between Variables | |

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Fitting a Line by Least Squares | |

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Applying the Least Squares Principle | |

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The Sample Correlation and Coefficient of Determination | |

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Computing and Using Residuals | |

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Some Cautions | |

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Computing | |

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Fitting Curves and Surfaces by Least Squares | |

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Curve Fitting by Least Squares | |

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Surface Fitting by Least Squares | |

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Some Additional Cautions | |

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Fitted Effects for Factorial Data | |

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Fitted Effects for 2-Factor Studies | |

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Simpler Descriptions for Some Two-Way Data Sets | |

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Fitted Effects for Three-Way (and Higher) Factorials | |

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Simpler Descriptions of Some Three-Way Data Sets | |

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Special Devices for 2[superscript p] Studies | |

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Transformations and Choice of Measurement Scale (Optional) | |

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Transformations and Single Samples | |

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Transformations and Multiple Samples | |

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Transformations and Simple Structure in Multifactor Studies | |

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Beyond Descriptive Statistics | |

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Probability: The Mathematics of Randomness | |

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(Discrete) Random Variables | |

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Random Variables and Their Distributions | |

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Discrete Probability Functions and Cumulative Probability Functions | |

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Summarization of Discrete Probability Distributions | |

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The Binomial and Geometric Distributions | |

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The Poisson Distributions | |

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Continuous Random Variables | |

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Probability Density Functions and Cumulative Probability Functions | |

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Means and Variances for Continuous Distributions | |

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The Normal Probability Distributions | |

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The Exponential Distributions (Optional) | |

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The Weibull Distributions (Optional) | |

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Probability Plotting (Optional) | |

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More on Normal Probability Plots | |

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Probability Plots for Exponential and Weibull Distributions | |

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Joint Distributions and Independence | |

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Describing Jointly Discrete Random Variables | |

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Conditional Distributions and Independence for Discrete Random Variables | |

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Describing Jointly Continuous Random Variables (Optional) | |

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Conditional Distributions and Independence for Continuous Random Variables (Optional) | |

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Functions of Several Random Variables | |

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The Distribution of a Function of Random Variables | |

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Simulations to Approximate the Distribution of U = g(X, Y,..., Z) | |

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Means and Variances for Linear Combinations of Random Variables | |

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The Propagation of Error Formulas | |

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The Central Limit Effect | |

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Introduction to Formal Statistical Inference | |

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Large-Sample Confidence Intervals for a Mean | |

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A Large-n Confidence Interval for [mu] Involving [sigma] | |

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A Generally Applicable Large-n Confidence Interval for [mu] | |

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Some Additional Comments Concerning Confidence Intervals | |

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Large-Sample Significance Tests for a Mean | |

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Large-n Significance Tests for [mu] Involving [sigma] | |

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A Five-Step Format for Summarizing Significance Tests | |

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Generally Applicable Large-n Significance Tests for [mu] | |

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Significance Testing and Formal Statistical Decision Making (Optional) | |

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Some Comments Concerning Significance Testing and Estimation | |

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One- and Two-Sample Inference for Means | |

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Small-Sample Inference for a Single Mean | |

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Inference for a Mean of Paired Differences | |

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Large-Sample Comparisons of Two Means (Based on Independent Samples) | |

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Small-Sample Comparisons of Two Means (Based on Independent Samples from Normal Distributions) | |

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One- and Two-Sample Inference for Variances | |

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Inference for the Variance of a Normal Distribution | |

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Inference for the Ratio of Two Variances (Based on Independent Samples from Normal Distributions) | |

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One- and Two-Sample Inference for Proportions | |

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Inference for a Single Proportion | |

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Inference for the Difference Between Two Proportions (Based on Independent Samples) | |

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Prediction and Tolerance Intervals | |

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Prediction Intervals for a Normal Distribution | |

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Tolerance Intervals for a Normal Distribution | |

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Prediction and Tolerance Intervals Based on Minimum and/or Maximum Values in a Sample | |

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Inference for Unstructured Multisample Studies | |

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The One-Way Normal Model | |

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Graphical Comparison of Several Samples of Measurement Data | |

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The One-Way (Normal) Multisample Model, Fitted Values, and Residuals | |

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A Pooled Estimate of Variance for Multisample Studies | |

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Standardized Residuals | |

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Simple Confidence Intervals in Multisample Studies | |

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Intervals for Means and for Comparing Means | |

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Intervals for General Linear Combinations of Means | |

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Individual and Simultaneous Confidence Levels | |

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Two Simultaneous Confidence Interval Methods | |

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The Pillai-Ramachandran Method | |

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Tukey's Method | |

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One-Way Analysis of Variance (ANOVA) | |

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Significance Testing and Multisample Studies | |

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The One-Way ANOVA F Test | |

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The One-Way ANOVA Identity and Table | |

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Random Effects Models and Analyses (Optional) | |

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ANOVA-Based Inference for Variance Components (Optional) | |

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Shewhart Control Charts for Measurement Data | |

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Generalities about Shewhart Control Charts | |

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"Standards Given" x Control Charts | |

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Retrospective x Control Charts | |

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Control Charts for Ranges | |

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Control Charts for Standard Deviations | |

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Control Charts for Measurements and Industrial Process Improvement | |

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Shewhart Control Charts for Qualitative and Count Data | |

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p Charts | |

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u Charts | |

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Common Control Chart Patterns and Special Checks | |

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Inference for Full and Fractional Factorial Studies | |

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Basic Inference in Two-Way Factorials with Some Replication | |

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One-Way Methods in Two-Way Factorials | |

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Two-Way Factorial Notation and Definitions of Effects | |

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Individual Confidence Intervals for Factorial Effects | |

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Tukey's Method for Comparing Main Effects (Optional) | |

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p-Factor Studies with Two Levels for Each Factor | |

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One-Way Methods in p-Way Factorials | |

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p-Way Factorial Notation, Definitions of Effects, and Related Confidence Interval Methods | |

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2[superscript p] Studies Without Replication and the Normal-Plotting of Fitted Effects | |

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Fitting and Checking Simplified Models in Balanced 2[superscript p] Factorial Studies and a Corresponding Variance Estimate (Optional) | |

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Confidence Intervals for Balanced 2[superscript p] Studies under Few-Effects Models (Optional) | |

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Standard Fractions of Two-Level Factorials, Part I: 1/2 Fractions | |

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General Observations about Fractional Factorial Studies | |

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Choice of Standard 1/2 Fractions of 2[superscript p] Studies | |

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Aliasing in the Standard 1/2 Fractions | |

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Data Analysis for 2[superscript p-1] Fractional Factorials | |

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Some Additional Comments | |

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Standard Fractions of Two-Level Factorials Part II: General 2[superscript p-q] Studies | |

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Using 2[superscript p-q] Fractional Factorials | |

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Design Resolution | |

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Two-Level Factorials and Fractional Factorials in Blocks (Optional) | |

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Some Additional Comments | |

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Regression Analysis--Inference for Curve- and Surface-Fitting | |

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Inference Methods Related to the Least Squares Fitting of a Line (Simple Linear Regression) | |

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The Simple Linear Regression Model, Corresponding Variance Estimate, and Standardized Residuals | |

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Inference for the Slope Parameter | |

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Inference for the Mean System Response for a Particular Value of x | |

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Prediction and Tolerance Intervals (Optional) | |

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Simple Linear Regression and ANOVA | |

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Simple Linear Regression and Statistical Software | |

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Inference Methods for General Least Squares Curve- and Surface-Fitting (Multiple Linear Regression) | |

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The Multiple Linear Regression Model, Corresponding Variance Estimate, and Standardized Residuals | |

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Inference for the Parameters [beta subscript 0], [beta subscript 1], [beta subscript 2],..., [beta subscript k] | |

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Inference for the Mean System Response for a Particular Set of Values for x[subscript 1], x[subscript 2],..., x[subscript k] | |

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Prediction and Tolerance Intervals (Optional) | |

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Multiple Regression and ANOVA | |

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Application of Multiple Regression in Response Surface Problems and Factorial Analyses | |

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Surface-Fitting and Response Surface Studies | |

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Regression and Factorial Analyses | |

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More on Probability and Model Fitting | |

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More Elementary Probability | |

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Basic Definitions and Axioms | |

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Simple Theorems of Probability Theory | |

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Conditional Probability and the Independence of Events | |

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Applications of Simple Probability to System Reliability Prediction | |

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Series Systems | |

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Parallel Systems | |

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Combination Series-Parallel Systems | |

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Counting | |

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A Multiplication Principle, Permutations, and Combinations | |

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Probabilistic Concepts Useful in Survival Analysis | |

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Survivorship and Force-of-Mortality Functions | |

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Maximum Likelihood Fitting of Probability Models and Related Inference Methods | |

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Likelihood Functions for Discrete Data and Maximum Likelihood Model Fitting | |

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Likelihood Functions for Continuous and Mixed Data and Maximum Likelihood Model Fitting | |

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Likelihood-Based Large-Sample Inference Methods | |

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Tables | |

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Answers to Section Exercises | |

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Index | |