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Applied Statistics and Probability for Engineers, 5th Edition

Book Description

Montgomery and Runger's best-selling engineering statistics text provides a practical approach oriented to engineering as well as chemical and physical sciences. By providing unique problem sets that reflect realistic situations, students learn how the material will be relevant in their careers and is suitable for a one- or two-term course in probability and statistics.

With a focus on how statistical tools are integrated into the engineering problem-solving process, all major aspects of engineering statistics are covered, including descriptive statistics, probability and probability distributions, statistical test and confidence intervals for one and two samples, building regression models, designing and analyzing engineering experiments, and statistical process control.

Developed with sponsorship from the National Science Foundation, this text incorporates many insights from the authors' teaching experience along with feedback from numerous adopters of previous editions.

Table of Contents

  1. Coverpage
  2. Titlepage
  3. Copyright
  4. Contents
  5. Preface
  6. INSIDE FRONT COVER Index of Applications in Examples and Exercises
  7. CHAPTER 1 The Role of Statistics in Engineering
    1. 1-1 The Engineering Method and Statistical Thinking
    2. 1-2 Collecting Engineering Data
      1. 1-2.1 Basic Principles
      2. 1-2.2 Retrospective Study
      3. 1-2.3 Observational Study
      4. 1-2.4 Designed Experiments
      5. 1-2.5 Observing Processes Over Time
    3. 1-3 Mechanistic and Empirical Models
    4. 1-4 Probability and Probability Models
  8. CHAPTER 2 Probability
    1. 2-1 Sample Spaces and Events
      1. 2-1.1 Random Experiments
      2. 2-1.2 Sample Spaces
      3. 2-1.3 Events
      4. 2-1.4 Counting Techniques
    2. 2-2 Interpretations and Axioms of Probability
    3. 2-3 Addition Rules
    4. 2-4 Conditional Probability
    5. 2-5 Multiplication and Total Probability Rules
    6. 2-6 Independence
    7. 2-7 Bayes’ Theorem
    8. 2-8 Random Variables
  9. CHAPTER 3 Discrete Random Variables and Probability Distributions
    1. 3-1 Discrete Random Variables
    2. 3-2 Probability Distributions and Probability Mass Functions
    3. 3-3 Cumulative Distribution Functions
    4. 3-4 Mean and Variance of a Discrete Random Variable
    5. 3-5 Discrete Uniform Distribution
    6. 3-6 Binomial Distribution
    7. 3-7 Geometric and Negative Binomial Distributions
    8. 3-8 Hypergeometric Distribution
    9. 3-9 Poisson Distribution
  10. CHAPTER 4 Continuous Random Variables and Probability Distributions
    1. 4-1 Continuous Random Variables
    2. 4-2 Probability Distributions and Probability Density Functions
    3. 4-3 Cumulative Distribution Functions
    4. 4-4 Mean and Variance of a Continuous Random Variable
    5. 4-5 Continuous Uniform Distribution
    6. 4-6 Normal Distribution
    7. 4-7 Normal Approximation to the Binomial and Poisson Distributions
    8. 4-8 Exponential Distribution
    9. 4-9 Erlang and Gamma Distributions
    10. 4-10 Weibull Distribution
    11. 4-11 Lognormal Distribution
    12. 4-12 Beta Distribution
  11. CHAPTER 5 Joint Probability Distributions
    1. 5-1 Two or More Random Variables
      1. 5-1.1 Joint Probability Distributions
      2. 5-1.2 Marginal Probability Distributions
      3. 5-1.3 Conditional Probability Distributions
      4. 5-1.4 Independence
      5. 5-1.5 More Than Two Random Variables
    2. 5-2 Covariance and Correlation
    3. 5-3 Common Joint Distributions
      1. 5-3.1 Multinomial Distribution
      2. 5-3.2 Bivariate Normal Distribution
    4. 5-4 Linear Functions of Random Variables
    5. 5-5 General Functions of Random Variables
  12. CHAPTER 6 Descriptive Statistics
    1. 6-1 Numerical Summaries of Data
    2. 6-2 Stem-and-Leaf Diagrams
    3. 6-3 Frequency Distributions and Histograms
    4. 6-4 Box Plots
    5. 6-5 Time Sequence Plots
    6. 6-6 Probability Plots
  13. CHAPTER 7 Sampling Distributions and Point Estimation of Parameters
    1. 7-1 Point Estimation
    2. 7-2 Sampling Distributions and the Central Limit Theorem
    3. 7-3 General Concepts of Point Estimation
      1. 7-3.1 Unbiased Estimators
      2. 7-3.2 Variance of a Point Estimator
      3. 7-3.3 Standard Error: Reporting a Point Estimate
      4. 7-3.4 Mean Squared Error of an Estimator
    4. 7-4 Methods of Point Estimation
      1. 7-4.1 Method of Moments
      2. 7-4.2 Method of Maximum Likelihood
      3. 7-4.3 Bayesian Estimation of Parameters
  14. CHAPTER 8 Statistical Intervals for a Single Sample
    1. 8-1 Confidence Interval on the Mean of a Normal Distribution, Variance Known
      1. 8-1.1 Development of the Confidence Interval and Its Basic Properties
      2. 8-1.2 Choice of Sample Size
      3. 8-1.3 One-sided Confidence Bounds
      4. 8-1.4 General Method to Derive a Confidence Interval
      5. 8-1.5 Large-Sample Confidence Interval for μ
    2. 8-2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown
      1. 8-2.1 t Distribution
      2. 8-2.2 t Confidence Interval on μ
    3. 8-3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution
    4. 8-4 Large-Sample Confidence Interval for a Population Proportion
    5. 8-5 Guidelines for Constructing Confidence Intervals
    6. 8-6 Tolerance and Prediction Intervals
      1. 8-6.1 Prediction Interval for a Future Observation
      2. 8-6.2 Tolerance Interval for a Normal Distribution
  15. CHAPTER 9 Tests of Hypotheses for a Single Sample
    1. 9-1 Hypothesis Testing
      1. 9-1.1 Statistical Hypotheses
      2. 9-1.2 Tests of Statistical Hypotheses
      3. 9-1.3 One-Sided and Two-Sided Hypothesis
      4. 9-1.4 P-Values in Hypothesis Tests
      5. 9-1.5 Connection between Hypothesis Tests and Confidence Intervals
      6. 9-1.6 General Procedure for Hypothesis Tests
    2. 9-2 Tests on the Mean of a Normal Distribution, Variance Known
      1. 9-2.1 Hypothesis Tests on the Mean
      2. 9-2.2 Type II Error and Choice of Sample Size
      3. 9-2.3 Large-Sample Test
    3. 9-3 Tests on the Mean of a Normal Distribution, Variance Unknown
      1. 9-3.1 Hypothesis Tests on the Mean
      2. 9-3.2 Type II Error and Choice of Sample Size
    4. 9-4 Tests on the Variance and Standard Deviation of a Normal Distribution
      1. 9-4.1 Hypothesis Tests on the Variance
      2. 9-4.2 Type II Error and Choice of Sample Size
    5. 9-5 Tests on a Population Proportion
      1. 9-5.1 Large-Sample Tests on a Proportion
      2. 9-5.2 Type II Error and Choice of Sample Size
    6. 9-6 Summary Table of Inference Procedures for a Single Sample
    7. 9-7 Testing for Goodness of Fit
    8. 9-8 Contingency Table Tests
    9. 9-9 Nonparametric Procedures
      1. 9-9.1 The Sign Test
      2. 9-9.2 The Wilcoxon Signed-Rank Test
      3. 9-9.3 Comparison to the t-Test
  16. CHAPTER 10 Statistical Inference for Two Samples
    1. 10-1 Inference on the Difference in Means of Two Normal Distributions, Variances Known
      1. 10-1.1 Hypothesis Tests on the Difference in Means, Variances Known
      2. 10-1.2 Type II Error and Choice of Sample Size
      3. 10-1.3 Confidence Interval on the Difference in Means, Variances Known
    2. 10-2 Inference on the Difference in Means of Two Normal Distributions, Variances Unknown
      1. 10-2.1 Hypothesis Tests on the Difference in Means, Variances Unknown
      2. 10-2.2 Type II Error and Choice of Sample Size
      3. 10-2.3 Confidence Interval on the Difference in Means, Variances Unknown
    3. 10-3 A Nonparametric Test for the Difference in Two Means
      1. 10-3.1 Description of the Wilcoxon Rank-Sum Test
      2. 10-3.2 Large-Sample Approximation
      3. 10-3.3 Comparison to the t-Test
    4. 10-4 Paired t-Test
    5. 10-5 Inference on the Variances of Two Normal Distributions
      1. 10-5.1 F Distribution
      2. 10-5.2 Hypothesis Tests on the Ratio of Two Variances
      3. 10-5.3 Type II Error and Choice of Sample Size
      4. 10-5.4 Confidence Interval on the Ratio of Two Variances
    6. 10-6 Inference on Two Population Proportions
      1. 10-6.1 Large-Sample Tests on the Difference in Population Proportions
      2. 10-6.2 Type II Error and Choice of Sample Size
      3. 10-6.3 Confidence Interval on the Difference in Population Proportions
    7. 10-7 Summary Table and Roadmap for Inference Procedures for Two Samples
  17. CHAPTER 11 Simple Linear Regression and Correlation
    1. 11-1 Empirical Models
    2. 11-2 Simple Linear Regression
    3. 11-3 Properties of the Least Squares Estimators
    4. 11-4 Hypothesis Tests in Simple Linear Regression
      1. 11-4.1 Use of t-Tests
      2. 11-4.2 Analysis of Variance Approach to Test Significance of Regression
    5. 11-5 Confidence Intervals
      1. 11-5.1 Confidence Intervals on the Slope and Intercept
      2. 11-5.2 Confidence Interval on the Mean Response
    6. 11-6 Prediction of New Observations
    7. 11-7 Adequacy of the Regression Model
      1. 11-7.1 Residual Analysis
      2. 11-7.2 Coefficient of Determination (R2)
    8. 11-8 Correlation
    9. 11-9 Regression on Transformed Variables
    10. 11-10 Logistic Regression
  18. CHAPTER 12 Multiple Linear Regression
    1. 12-1 Multiple Linear Regression Model
      1. 12-1.1 Introduction
      2. 12-1.2 Least Squares Estimation of the Parameters
      3. 12-1.3 Matrix Approach to Multiple Linear Regression
      4. 12-1.4 Properties of the Least Squares Estimators
    2. 12-2 Hypothesis Tests in Multiple Linear Regression
      1. 12-2.1 Test for Significance of Regression
      2. 12-2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients
    3. 12-3 Confidence Intervals in Multiple Linear Regression
      1. 12-3.1 Confidence Intervals on Individual Regression Coefficients
      2. 12-3.2 Confidence Interval on the Mean Response
    4. 12-4 Prediction of New Observations
    5. 12-5 Model Adequacy Checking
      1. 12-5.1 Residual Analysis
      2. 12-5.2 Influential Observations
    6. 12-6 Aspects of Multiple Regression Modeling
      1. 12-6.1 Polynomial Regression Models
      2. 12-6.2 Categorical Regressors and Indicator Variables
      3. 12-6.3 Selection of Variables and Model Building
      4. 12-6.4 Multicollinearity
  19. CHAPTER 13 Design and Analysis of Single-Factor Experiments: The Analysis of Variance
    1. 13-1 Designing Engineering Experiments
    2. 13-2 Completely Randomized Single-Factor Experiment
      1. 13-2.1 Example: Tensile Strength
      2. 13-2.2 Analysis of Variance
      3. 13-2.3 Multiple Comparisons Following the ANOVA
      4. 13-2.4 Residual Analysis and Model Checking
      5. 13-2.5 Determining Sample Size
    3. 13-3 The Random-Effects Model
      1. 13-3.1 Fixed Versus Random Factors
      2. 13-3.2 ANOVA and Variance Components
    4. 13-4 Randomized Complete Block Design
      1. 13-4.1 Design and Statistical Analysis
      2. 13-4.2 Multiple Comparisons
      3. 13-4.3 Residual Analysis and Model Checking
  20. CHAPTER 14 Design of Experiments with Several Factors
    1. 14-1 Introduction
    2. 14-2 Factorial Experiments
    3. 14-3 Two-Factor Factorial Experiments
      1. 14-3.1 Statistical Analysis of the Fixed-Effects Model
      2. 14-3.2 Model Adequacy Checking
      3. 14-3.3 One Observation per Cell
    4. 14-4 General Factorial Experiments
    5. 14-5 2k Factorial Designs
      1. 14-5.1 22 Design
      2. 14-5.2 2k Design for k ≥ 3 Factors
      3. 14-5.3 Single Replicate of the 2k Design
      4. 14-5.4 Addition of Center Points to a 2k Design
    6. 14-6 Blocking and Confounding in the 2k Design
    7. 14-7 Fractional Replication of the 2k Design
      1. 14-7.1 One-Half Fraction of the 2k Design
      2. 14-7.2 Smaller Fractions: The 2k−p Fractional Factorial
    8. 14-8 Response Surface Methods and Designs
  21. CHAPTER 15 Statistical Quality Control
    1. 15-1 Quality Improvement and Statistics
      1. 15-1.1 Statistical Quality Control
      2. 15-1.2 Statistical Process Control
    2. 15-2 Introduction to Control Charts
      1. 15-2.1 Basic Principles
      2. 15-2.2 Design of a Control Chart
      3. 15-2.3 Rational Subgroups
      4. 15-2.4 Analysis of Patterns on Control Charts
    3. 15-3 X and R or S Control Charts
    4. 15-4 Control Charts for Individual Measurements
    5. 15-5 Process Capability
    6. 15-6 Attribute Control Charts
      1. 15-6.1 P Chart (Control Chart for Proportions)
      2. 15-6.2 U Chart (Control Chart for Defects per Unit)
    7. 15-7 Control Chart Performance
    8. 15-8 Time-Weighted Charts
      1. 15-8.1 Cumulative Sum Control Chart
      2. 15-8.2 Exponentially Weighted Moving Average Control Chart
    9. 15-9 Other SPC Problem-Solving Tools
    10. 15-10 Implementing SPC
  22. APPENDICES
    1. APPENDIX A: Statistical Tables and Charts
      1. Table I Summary of Common Probability Distributions
      2. Table II Cumulative Binomial Probability P(X ≤ x)
      3. Table III Cumulative Standard Normal Distribution
      4. Table IV Percentage Points χ2α, v of the Chi-Squared Distribution
      5. Table V Percentage Points tα, v of the t distribution
      6. Table VI Percentage Points fα, v1,v2 of the F distribution
      7. Chart VII Operating Characteristic Curves
      8. Table VIII Critical Values for the Sign Test
      9. Table IX Critical Values for the Wilcoxon Signed-Rank Test
      10. Table X Critical Values for the Wilcoxon Rank-Sum Test
      11. Table XI Factors for Constructing Variables Control Charts
      12. Table XII Factors for Tolerance Intervals
    2. APPENDIX B: Answers to Selected Exercises
    3. APPENDIX C: Bibliography
  23. GLOSSARY
  24. INDEX
  25. INDEX OF APPLICATIONS IN EXAMPLES AND EXERCISES, CONTINUED