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The Role of Statistics in Engineering | |

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The Engineering Method and Statistical Thinking | |

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Collecting Engineering Data | |

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Basic Principles | |

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Retrospective Study | |

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Observational Study | |

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Designed Experiments | |

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Observing Processes Over Time | |

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Mechanistic and Empirical Models | |

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Probability and Probability Models | |

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Probability | |

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Sample Spaces and Events | |

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Random Experiments | |

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Sample Spaces | |

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Events | |

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Counting Techniques | |

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Interpretations of Probability | |

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Introduction | |

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Axioms of Probability | |

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Addition Rules | |

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Conditional Probability | |

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Multiplication and Total Probability Rules | |

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Multiplication Rule | |

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Total Probability Rule | |

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Independence | |

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Bayes' Theorem | |

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Random Variables | |

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Discrete Random Variables and Probability Distributions | |

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Discrete Random Variables | |

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Probability Distributions and Probability Mass Functions | |

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Cumulative Distribution Functions | |

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Mean and Variance of a Discrete Random Variable | |

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Discrete Uniform Distribution | |

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Binomial Distribution | |

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Geometric and Negative Binomial Distributions | |

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Geometric Distribution | |

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Negative Binomial Distribution | |

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Hypergeometric Distribution | |

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Poisson Distribution | |

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Continuous Random Variables and Probability Distributions | |

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Continuous Random Variables | |

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Probability Distributions and Probability Density Functions | |

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Cumulative Distribution Functions | |

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Mean and Variance of a Continuous Random Variable | |

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Continuous Uniform Distribution | |

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Normal Distribution | |

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Normal Approximation to the Binomial and Poisson Distributions | |

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Exponential Distribution | |

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Erlang and Gamma Distributions | |

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Weibull Distribution | |

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Lognormal Distribution | |

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Joint Probability Distributions | |

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Two or More Discrete Random Variables | |

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Joint Probability Distributions | |

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Marginal Probability Distributions | |

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Conditional Probability Distributions | |

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Independence | |

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Multiple Discrete Random Variables | |

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Multinomial Probability Distribution | |

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Two or More Continuous Random Variables | |

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Joint Probability Distributions | |

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Marginal Probability Distributions | |

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Conditional Probability Distributions | |

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Independence | |

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Multiple Continuous Random Variables | |

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Covariance and Correlation | |

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Bivariate Normal Distribution | |

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Linear Functions of Random Variables | |

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Several Functions of Random Variables | |

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Random Sampling and Data Description | |

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Numerical Summaries | |

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Stem-and-Leaf Diagrams | |

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Frequency Distributions and Histograms | |

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Box Plots | |

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Time Sequence Plots | |

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Probability Plots | |

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Sampling Distributions and Point Estimation of Parameters | |

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Introduction | |

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Sampling Distributions and the Central Limit Theorem | |

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General Concepts of Point Estimation | |

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Unbiased Estimators | |

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Variance of a Point Estimator | |

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Standard Error: Reporting a Point Estimator | |

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Mean Squared Error of an Estimator | |

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Methods of Point Estimation | |

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Method of Moments | |

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Method of Maximum Likelihood | |

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Bayesian Estimation of Parameters | |

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Statistical Intervals for a Single Sample | |

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Introduction | |

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Confidence Interval on the Mean of a Normal Distribution, Variance Known | |

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Development of the Confidence Interval and Its Basic Properties | |

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Choice of Sample Size | |

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One-sided Confidence Bounds | |

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General Method to Derive a Confidence Interval | |

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Large-Sample Confidence Interval for [mu] | |

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Confidence Interval on the Mean of a Normal Distribution, Variance Unknown | |

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t Distribution | |

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t Confidence Interval on [mu] | |

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Confidence Interval on the Variance and Standard Deviation of a Normal Distribution | |

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Large-Sample Confidence Interval for a Population Proportion | |

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Guidelines for Constructing Confidence Intervals | |

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Tolerance and Prediction Intervals | |

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Prediction Interval for a Future Observation | |

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Tolerance Interval for a Normal Distribution | |

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Tests of Hypotheses for a Single Sample | |

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Hypothesis Testing | |

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Statistical Hypotheses | |

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Tests of statistical Hypotheses | |

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One-Sided and Two-Sided Hypothesis | |

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P-Values in Hypothesis Tests | |

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Connection between Hypothesis Tests and Confidence Intervals | |

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General Procedure for Hypothesis Tests | |

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Tests on the Mean of a Normal Distribution, Variance Known | |

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Hypothesis Tests on the Mean | |

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Type II Error and Choice of Sample Size | |

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Large Sample Test | |

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Tests on the Mean of a Normal Distribution, Variance Unknown | |

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Hypothesis Tests on the Mean | |

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P-Value for a t-Test | |

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Type II Error and Choice of Sample Size | |

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Tests on the Variance and Standard Deviation of a Normal Distribution | |

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Hypothesis Tests on the Variance | |

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Type II Error and Choice of Sample Size | |

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Tests on a Population Proportion | |

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Large-Sample Tests on a Proportion | |

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Type II Error and Choice of Sample Size | |

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Summary Table of Inference Procedures for a Single Sample | |

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Testing for Goodness of Fit | |

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Contingency Table Tests | |

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Statistical Inference for Two Samples | |

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Introduction | |

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Inference on the Difference in Means of Two Normal Distributions, Variances Known | |

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Hypothesis Tests on the Difference in Means, Variances Known | |

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Type II Error and Choice of Sample Size | |

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Confidence Interval on the Difference in Means, Variances Known | |

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Inference on the Difference in Means of Two Normal Distributions, Variances Unknown | |

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Hypothesis Tests on the Difference in Means, Variances Unknown | |

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Type II Error and Choice of Sample Size | |

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Confidence Interval on the Difference in Means, Variances Unknown | |

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Paired t-Test | |

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Inference on the Variances of Two Normal Distributions | |

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F Distribution | |

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Hypothesis Tests on the Ratio of Two Variances | |

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Type II Error and Choice of Sample Size | |

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Confidence Interval on the Ratio of Two Variances | |

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Inference on Two Population Proportions | |

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Large-Sample Tests on the Difference in Population Proportions | |

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Type II Error and Choice of Sample Size | |

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Confidence Interval on the Difference in Population Proportions | |

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Summary Table and Roadmaps for Inference Procedures for Two Samples | |

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Simple Linear Regression and Correlation | |

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Empirical Models | |

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Simple Linear Regression | |

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Properties of the Least Squares Estimators | |

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Hypothesis Tests in Simple Linear Regression | |

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Use of t-Tests | |

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Analysis of Variance Approach to Test Significance of Regression | |

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Confidence Intervals | |

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Confidence Intervals on the Slope and Intercept | |

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Confidence Interval on the Mean Response | |

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Prediction of New Observations | |

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Adequacy of the Regression Model | |

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Residual Analysis | |

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Coefficient of Determination (R[superscript 2]) | |

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Correlation | |

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Transformations | |

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Logistic Regression available at www.wiley.com/college/montgomery | |

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Multiple Linear Regression | |

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Multiple Linear Regression Model | |

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Introduction | |

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Least Squares Estimation of the Parameters | |

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Matrix Approach to Multiple Linear Regression | |

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Properties of the Least Squares Estimators | |

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Hypothesis Tests in Multiple Linear Regression | |

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Test for Significance of Regression | |

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Tests on Individual Regression Coefficients and Subsets of Coefficients | |

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Confidence Intervals in Multiple Linear Regression | |

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Confidence Intervals on Individual Regression Coefficients | |

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Confidence Interval on the Mean Response | |

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Prediction of New Observations | |

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Model Adequacy Checking | |

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Residual Analysis | |

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Influential Observations | |

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Aspects of Multiple Regression Modeling | |

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Polynomial Regression Models | |

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Categorical Regressors and Indicator Variables | |

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Selection of Variables and Model Building | |

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Multicollinearity | |

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Design and Analysis of Single-Factor Experiments: The Analysis of Variance | |

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Designing Engineering Experiments | |

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Completely Randomized Single-Factor Experiment | |

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Example: Tensile Strength | |

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Analysis of Variance | |

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Multiple Comparisons Following the ANOVA | |

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Residual Analysis and Model Checking | |

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Determining Sample Size | |

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Random Effects Model | |

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Fixed Versus Random Factors | |

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ANOVA and Variance Components | |

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Randomized Complete Block Design | |

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Design and Statistical Analysis | |

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Multiple Comparisons | |

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Residual Analysis and Model Checking | |

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Design of Experiments with Several Factors | |

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Introduction | |

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Factorial Experiments | |

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Two-Factor Factorial Experiments | |

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Statistical Analysis of the Fixed-Effects Model | |

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Model Adequacy Checking | |

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One Observation Per Cell | |

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General Factorial Experiments | |

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2[superscript k] Factorial Designs | |

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2[superscript 2] Design | |

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2[superscript k] Design for k [greater than or equal] 3 Factors | |

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Single Replicate of the 2[superscript k] Design | |

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Addition of Center Points to a 2[superscript k] Design | |

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Blocking and Confounding in the 2[superscript k] Design | |

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Fractional Replication of the 2[superscript k] Design | |

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One Half Fraction of the 2[superscript k] Design | |

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Smaller Fractions: The 2[superscript k-p] Fractional Factorial | |

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Response Surface Methods and Designs | |

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Nonparametric Statistics | |

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Introduction | |

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Sign Test | |

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Description of the Test | |

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Sign Test for Paired Samples | |

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Type II Error for the Sign Test | |

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Comparison to the t-Test | |

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Wilcoxon Signed-Rank Test | |

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Description of the Test | |

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Large-Sample Approximation | |

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Paired Observations | |

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Comparison to the t-Test | |

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Wilcoxon Rank-Sum Test | |

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Description of the Test | |

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Large-Sample Approximation | |

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Comparison to the t-Test | |

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Nonparametric Methods in the Analysis of Variance | |

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Kruskal-Wallis Test | |

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Rank Transformation | |

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Runs Test | |

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Statistical Quality Control | |

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Quality Improvement and Statistics | |

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Statistical Quality Control | |

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Statistical Process Control | |

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Introduction to Control Charts | |

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Basic Principles | |

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Design of a Control Chart | |

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Rational Subgroups | |

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Analysis of Patterns on Control Charts | |

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X and R or S Control Charts | |

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Control Charts for Individual Measurements | |

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Process Capability | |

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Attribute Control Charts | |

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P Chart (Control Chart for Proportion) | |

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U Chart (Control Chart for Defects per Unit) | |

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Control Chart Performance | |

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Time-Weighted Charts | |

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Cumulative Sum Control Chart | |

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Exponentially Weighted Moving Average Control Chart | |

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Other SPC Problem-Solving Tools | |

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Implementing SPC | |

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Appendices | |

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Statistical Tables and Charts | |

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Summary of Common Probability Distributions | |

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Cumulative Binomial Distribution | |

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Cumulative Standard Normal Distribution | |

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Percentage Points [characters not reproducible] of the Chi-Squared Distribution | |

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Percentage Points t[subscript alpha, upsilon] of the t-distribution | |

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Percentage Points [characters not reproducible] of the F-distribution | |

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Operating Characteristic Curves | |

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Critical Values for the Sign Test | |

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Critical Values for the Wilcoxon Signed-Rank Test | |

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Critical Values for the Wilcoxon Rank-Sum Test | |

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Factors for Constructing Variables Control Charts | |

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Factors for Tolerance Intervals | |

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Answers to Selected Exercises | |

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Bibliography available at www.wiley.com/college/montgomery | |

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Glossary | |

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Index | |

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Applications in Examples and Exercises Continued | |