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Applied Statistics and Probability for Engineers, 5th Edition

Name: Applied Statistics and Probability for Engineers, 5th Edition
ISBN: 9780470053041

by George C. Runger, Douglas C. Montgomery

March 2010

Intermediate to advanced

784 pages

31h 22m

English

Wiley

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Coverpage
Titlepage
Copyright
Contents
Preface
INSIDE FRONT COVER Index of Applications in Examples and Exercises
CHAPTER 1 The Role of Statistics in Engineering
1-1 The Engineering Method and Statistical Thinking1-2 Collecting Engineering Data1-2.1 Basic Principles1-2.2 Retrospective Study1-2.3 Observational Study1-2.4 Designed Experiments1-2.5 Observing Processes Over Time1-3 Mechanistic and Empirical Models1-4 Probability and Probability Models
CHAPTER 2 Probability
2-1 Sample Spaces and Events2-1.1 Random Experiments2-1.2 Sample Spaces2-1.3 Events2-1.4 Counting Techniques2-2 Interpretations and Axioms of Probability2-3 Addition Rules2-4 Conditional Probability2-5 Multiplication and Total Probability Rules2-6 Independence2-7 Bayes’ Theorem2-8 Random Variables
CHAPTER 3 Discrete Random Variables and Probability Distributions
3-1 Discrete Random Variables3-2 Probability Distributions and Probability Mass Functions3-3 Cumulative Distribution Functions3-4 Mean and Variance of a Discrete Random Variable3-5 Discrete Uniform Distribution3-6 Binomial Distribution3-7 Geometric and Negative Binomial Distributions3-8 Hypergeometric Distribution3-9 Poisson Distribution
CHAPTER 4 Continuous Random Variables and Probability Distributions
4-1 Continuous Random Variables4-2 Probability Distributions and Probability Density Functions4-3 Cumulative Distribution Functions4-4 Mean and Variance of a Continuous Random Variable4-5 Continuous Uniform Distribution4-6 Normal Distribution4-7 Normal Approximation to the Binomial and Poisson Distributions4-8 Exponential Distribution4-9 Erlang and Gamma Distributions4-10 Weibull Distribution4-11 Lognormal Distribution4-12 Beta Distribution

CHAPTER 5 Joint Probability Distributions
5-1 Two or More Random Variables5-1.1 Joint Probability Distributions5-1.2 Marginal Probability Distributions5-1.3 Conditional Probability Distributions5-1.4 Independence5-1.5 More Than Two Random Variables5-2 Covariance and Correlation5-3 Common Joint Distributions5-3.1 Multinomial Distribution5-3.2 Bivariate Normal Distribution5-4 Linear Functions of Random Variables5-5 General Functions of Random Variables
CHAPTER 6 Descriptive Statistics
6-1 Numerical Summaries of Data6-2 Stem-and-Leaf Diagrams6-3 Frequency Distributions and Histograms6-4 Box Plots6-5 Time Sequence Plots6-6 Probability Plots
CHAPTER 7 Sampling Distributions and Point Estimation of Parameters
7-1 Point Estimation7-2 Sampling Distributions and the Central Limit Theorem7-3 General Concepts of Point Estimation7-3.1 Unbiased Estimators7-3.2 Variance of a Point Estimator7-3.3 Standard Error: Reporting a Point Estimate7-3.4 Mean Squared Error of an Estimator7-4 Methods of Point Estimation7-4.1 Method of Moments7-4.2 Method of Maximum Likelihood7-4.3 Bayesian Estimation of Parameters
CHAPTER 8 Statistical Intervals for a Single Sample
8-1 Confidence Interval on the Mean of a Normal Distribution, Variance Known8-1.1 Development of the Confidence Interval and Its Basic Properties8-1.2 Choice of Sample Size8-1.3 One-sided Confidence Bounds8-1.4 General Method to Derive a Confidence Interval8-1.5 Large-Sample Confidence Interval for μ8-2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown8-2.1 t Distribution8-2.2 t Confidence Interval on μ8-3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution8-4 Large-Sample Confidence Interval for a Population Proportion8-5 Guidelines for Constructing Confidence Intervals8-6 Tolerance and Prediction Intervals8-6.1 Prediction Interval for a Future Observation8-6.2 Tolerance Interval for a Normal Distribution
CHAPTER 9 Tests of Hypotheses for a Single Sample
9-1 Hypothesis Testing9-1.1 Statistical Hypotheses9-1.2 Tests of Statistical Hypotheses9-1.3 One-Sided and Two-Sided Hypothesis9-1.4 P-Values in Hypothesis Tests9-1.5 Connection between Hypothesis Tests and Confidence Intervals9-1.6 General Procedure for Hypothesis Tests9-2 Tests on the Mean of a Normal Distribution, Variance Known9-2.1 Hypothesis Tests on the Mean9-2.2 Type II Error and Choice of Sample Size9-2.3 Large-Sample Test9-3 Tests on the Mean of a Normal Distribution, Variance Unknown9-3.1 Hypothesis Tests on the Mean9-3.2 Type II Error and Choice of Sample Size9-4 Tests on the Variance and Standard Deviation of a Normal Distribution9-4.1 Hypothesis Tests on the Variance9-4.2 Type II Error and Choice of Sample Size9-5 Tests on a Population Proportion9-5.1 Large-Sample Tests on a Proportion9-5.2 Type II Error and Choice of Sample Size9-6 Summary Table of Inference Procedures for a Single Sample9-7 Testing for Goodness of Fit9-8 Contingency Table Tests9-9 Nonparametric Procedures9-9.1 The Sign Test9-9.2 The Wilcoxon Signed-Rank Test9-9.3 Comparison to the t-Test
CHAPTER 10 Statistical Inference for Two Samples
10-1 Inference on the Difference in Means of Two Normal Distributions, Variances Known10-1.1 Hypothesis Tests on the Difference in Means, Variances Known10-1.2 Type II Error and Choice of Sample Size10-1.3 Confidence Interval on the Difference in Means, Variances Known10-2 Inference on the Difference in Means of Two Normal Distributions, Variances Unknown10-2.1 Hypothesis Tests on the Difference in Means, Variances Unknown10-2.2 Type II Error and Choice of Sample Size10-2.3 Confidence Interval on the Difference in Means, Variances Unknown10-3 A Nonparametric Test for the Difference in Two Means10-3.1 Description of the Wilcoxon Rank-Sum Test10-3.2 Large-Sample Approximation10-3.3 Comparison to the t-Test10-4 Paired t-Test10-5 Inference on the Variances of Two Normal Distributions10-5.1 F Distribution10-5.2 Hypothesis Tests on the Ratio of Two Variances10-5.3 Type II Error and Choice of Sample Size10-5.4 Confidence Interval on the Ratio of Two Variances10-6 Inference on Two Population Proportions10-6.1 Large-Sample Tests on the Difference in Population Proportions10-6.2 Type II Error and Choice of Sample Size10-6.3 Confidence Interval on the Difference in Population Proportions10-7 Summary Table and Roadmap for Inference Procedures for Two Samples
CHAPTER 11 Simple Linear Regression and Correlation
11-1 Empirical Models11-2 Simple Linear Regression11-3 Properties of the Least Squares Estimators11-4 Hypothesis Tests in Simple Linear Regression11-4.1 Use of t-Tests11-4.2 Analysis of Variance Approach to Test Significance of Regression11-5 Confidence Intervals11-5.1 Confidence Intervals on the Slope and Intercept11-5.2 Confidence Interval on the Mean Response11-6 Prediction of New Observations11-7 Adequacy of the Regression Model11-7.1 Residual Analysis11-7.2 Coefficient of Determination (R2)11-8 Correlation11-9 Regression on Transformed Variables11-10 Logistic Regression
CHAPTER 12 Multiple Linear Regression
12-1 Multiple Linear Regression Model12-1.1 Introduction12-1.2 Least Squares Estimation of the Parameters12-1.3 Matrix Approach to Multiple Linear Regression12-1.4 Properties of the Least Squares Estimators12-2 Hypothesis Tests in Multiple Linear Regression12-2.1 Test for Significance of Regression12-2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients12-3 Confidence Intervals in Multiple Linear Regression12-3.1 Confidence Intervals on Individual Regression Coefficients12-3.2 Confidence Interval on the Mean Response12-4 Prediction of New Observations12-5 Model Adequacy Checking12-5.1 Residual Analysis12-5.2 Influential Observations12-6 Aspects of Multiple Regression Modeling12-6.1 Polynomial Regression Models12-6.2 Categorical Regressors and Indicator Variables12-6.3 Selection of Variables and Model Building12-6.4 Multicollinearity
CHAPTER 13 Design and Analysis of Single-Factor Experiments: The Analysis of Variance
13-1 Designing Engineering Experiments13-2 Completely Randomized Single-Factor Experiment13-2.1 Example: Tensile Strength13-2.2 Analysis of Variance13-2.3 Multiple Comparisons Following the ANOVA13-2.4 Residual Analysis and Model Checking13-2.5 Determining Sample Size13-3 The Random-Effects Model13-3.1 Fixed Versus Random Factors13-3.2 ANOVA and Variance Components13-4 Randomized Complete Block Design13-4.1 Design and Statistical Analysis13-4.2 Multiple Comparisons13-4.3 Residual Analysis and Model Checking
CHAPTER 14 Design of Experiments with Several Factors
14-1 Introduction14-2 Factorial Experiments14-3 Two-Factor Factorial Experiments14-3.1 Statistical Analysis of the Fixed-Effects Model14-3.2 Model Adequacy Checking14-3.3 One Observation per Cell14-4 General Factorial Experiments14-5 2k Factorial Designs14-5.1 22 Design14-5.2 2k Design for k ≥ 3 Factors14-5.3 Single Replicate of the 2k Design14-5.4 Addition of Center Points to a 2k Design14-6 Blocking and Confounding in the 2k Design14-7 Fractional Replication of the 2k Design14-7.1 One-Half Fraction of the 2k Design14-7.2 Smaller Fractions: The 2k−p Fractional Factorial14-8 Response Surface Methods and Designs
CHAPTER 15 Statistical Quality Control
15-1 Quality Improvement and Statistics15-1.1 Statistical Quality Control15-1.2 Statistical Process Control15-2 Introduction to Control Charts15-2.1 Basic Principles15-2.2 Design of a Control Chart15-2.3 Rational Subgroups15-2.4 Analysis of Patterns on Control Charts15-3 X and R or S Control Charts15-4 Control Charts for Individual Measurements15-5 Process Capability15-6 Attribute Control Charts15-6.1 P Chart (Control Chart for Proportions)15-6.2 U Chart (Control Chart for Defects per Unit)15-7 Control Chart Performance15-8 Time-Weighted Charts15-8.1 Cumulative Sum Control Chart15-8.2 Exponentially Weighted Moving Average Control Chart15-9 Other SPC Problem-Solving Tools15-10 Implementing SPC
APPENDICES
APPENDIX A: Statistical Tables and ChartsTable I Summary of Common Probability DistributionsTable II Cumulative Binomial Probability P(X ≤ x)Table III Cumulative Standard Normal DistributionTable IV Percentage Points χ2α, v of the Chi-Squared DistributionTable V Percentage Points tα, v of the t distributionTable VI Percentage Points fα, v1,v2 of the F distributionChart VII Operating Characteristic CurvesTable VIII Critical Values for the Sign TestTable IX Critical Values for the Wilcoxon Signed-Rank TestTable X Critical Values for the Wilcoxon Rank-Sum TestTable XI Factors for Constructing Variables Control ChartsTable XII Factors for Tolerance Intervals
APPENDIX B: Answers to Selected Exercises
APPENDIX C: Bibliography
GLOSSARY
INDEX
INDEX OF APPLICATIONS IN EXAMPLES AND EXERCISES, CONTINUED

Content preview from Applied Statistics and Probability for Engineers, 5th Edition

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An athletic woman in her twenties arrives at the emergency department complaining of dizziness after running in hot weather. An electrocardiogram is used to check for a heart attack and the patient generates an abnormal result. The test has a false positive rate 0.1 (the probability of an abnormal result when the patient is normal) and a false negative rate of 0.1 (the probability of a normal result when the patient is abnormal). Furthermore, it might be assumed that the prior probability of a heart attack for this patient is 0.001. Although the abnormal test is a concern, you might be surprised to learn that the probability of a heart attack given the electrocardiogram result is still less than 0.01. See “Why Clinicians are Natural Bayesians” (2005, bmj.com) for details of this example and others.

The key is to properly combine the given probabilities. Furthermore, the exact same analysis used for this medical example can be applied to tests of engineered products. Consequently knowledge of how to manipulate probabilities in order to assess risks and make better decisions is important throughout scientific and engineering disciplines. In this chapter the laws of probability are presented and used to assess risks in cases such as this one and numerous others.

CHAPTER OUTLINE

2-1 SAMPLE SPACES AND EVENTS

2-1.1 Random Experiments

2-1.2 Sample Spaces

2-1.3 Events

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Applied Statistics and Probability for Engineers, 5th Edition

by George C. Runger, Douglas C. Montgomery

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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