Normal 0 false false false KEY BENEFIT: This text is rich in exercises and examples, and explores both elementary probability and basic statistics, with an emphasis on engineering and science applications. Much of the data have been collected from the author's own consulting experience and from discussions with scientists and engineers about the use of statistics in their fields. In later chapters, the text emphasizes designed experiments, especially two-level factorial design. Introduction, Organization and Description of Data, Probability, Probability Distributions, Probability Densities, Sampling Distributions, Inferences Concerning a Mean, Comparing Two Treatments, Inferences Concerning Variances, Inferences Concerning Proportions, Regression Analysis, Analysis of Variance, Factorial Experimentation, Nonparametric Tests, The Statistical Content of Quality-Improvement Programs, Application to Reliability and Life Testing For all readers interested in probability and statistics for engineers.

Preface

**1. Introduction**

1.1 Why Study Statistics?

1.2 Modern Statistics

1.3 Statistics and Engineering

1.4 The Role of the Scientist and Engineer in Quality Improvement

1.5 A Case Study: Visually Inspecting Data to Improve Product Quality

1.6 Two Basic Concepts–Population and Sample

**2. Organization and Description of Data**

2.1 Pareto Diagrams and Dot Diagrams

2.2 Frequency Distributions

2.3 Graphs of Frequency Distributions

2.4 Stem-and-Leaf Displays

2.5 Descriptive Measures

2.6 Quartiles and Percentiles

2.7 The Calculation of *x* and *s*

2.8 A Case Study: Problems with Aggregating Data

**3. Probability**

3.1 Sample Spaces and Events

3.2 Counting

3.3 Probability

3.4 The Axioms of Probability

3.5 Some Elementary Theorems

3.6 Conditional Probability

3.7 Bayes’ Theorem

**4. Probability Distributions**

4.1 Random Variables

4.2 The Binomial Distribution

4.3 The Hypergeometric Distribution

4.4 The Mean and the Variance of a Probability Distribution

4.5 Chebyshev’s Theorem

4.6 The Poisson Approximation to the Binomial Distribution

4.7 Poisson Processes

4.8 The Geometric and Negative Binomial Distribution

4.9 The Multinomial Distribution

4.10 Simulation

**5. Probability Densities**

5.1 Continuous Random Variables

5.2 The Normal Distribution

5.3 The Normal Approximation to the Binomial Distribution

5.4 Other Probability Densities

5.5 The Uniform Distribution

5.6 The Log-Normal Distribution

5.7 The Gamma Distribution

5.8 The Beta Distribution

5.9 The Weibull Distribution

5.10 Joint Distributions–Discrete and Continuous

5.11 Moment Generating Functions

5.12 Checking If the Data Are Normal

5.13 Transforming Observations to Near Normality

5.14 Simulation

**6. Sampling Distributions**

6.1 Populations and Samples

6.2 The Sampling Distribution of the Mean (σ known)

6.3 The Sampling Distribution of the Mean (σ unknown)

6.4 The Sampling Distribution of the Variance

6.5 Representations of the Normal Theory Distributions

6.6 The Moment Generating Function Method to Obtain Distributions

6.7 Transformation Methods to Obtain Distributions

**7. Inferences Concerning a Mean**

7.1 Point Estimation

7.2 Interval Estimation

7.3 Maximum Likelihood Estimation

7.4 Tests of Hypotheses

7.5 Null Hypotheses and Tests of Hypotheses

7.6 Hypotheses Concerning One Mean

7.7 The Relation between Tests and Confidence Intervals

7.8 Power, Sample Size, and Operating Characteristic Curves

**8. Comparing Two Treatments**

8.1 Experimental Designs for Comparing Two Treatments

8.2 Comparisons–Two Independent Large Samples

8.3 Comparisons–Two Independent Small Samples

8.4 Matched Pairs Comparisons

8.5 Design Issues–Randomization and Pairing

**9. Inferences Concerning Variances**

9.1 The Estimation of Variances

9.2 Hypotheses Concerning One Variance

9.3 Hypotheses Concerning Two Variances

**10. Inferences Concerning Proportions**

10.1 Estimation of Proportions

10.2 Hypotheses Concerning One Proportion

10.3 Hypotheses Concerning Several Proportions

10.4 Analysis of *r* x *c* Tables

10.5 Goodness of Fit

**11. Regression Analysis**

11.1 The Method of Least Squares

11.2 Inferences Based on the Least Squares Estimators

11.3 Curvilinear Regression

11.4 Multiple Regression

11.5 Checking the Adequacy of the Model

11.6 Correlation

11.7 Multiple Linear Regression (Matrix Notation)

**12. Analysis of Variance**

12.1 Some General Principles

12.2 Completely Randomized Designs

12.3 Randomized-Block Designs

12.4 Multiple Comparisons

12.5 Analysis of Covariance

**13. Factorial Experimentation**

13.1 Two-Factor Experiments

13.2 Multifactor Experiments

13.3 2* *^{n} Factorial Experiments

13.4 The Graphic Presentation of 22 and 23 Experiments

13.5 Response Surface Analysis

13.6 Confounding in a 2* *^{n} Factorial Experiment

13.7 Fractional Replication

**14. Nonparametric Tests**

14.1 Introduction

14.2 The Sign Test

14.3 Rank-Sum Tests

14.4 Correlation Based on Ranks

14.5 Tests of Randomness

14.6 The Kolmogorov-Smirnov and Anderson-Darling Tests

**15. The Statistical Content of Quality-Improvement Programs**

15.1 Quality-Improvement Programs

15.2 Starting a Quality-Improvement Program

15.3 Experimental Designs for Quality

15.4 Quality Control

15.5 Control Charts for Measurements

15.6 Control Charts for Attributes

15.7 Tolerance Limits

**16. Application to Reliability and Life Testing**

16.1 Reliability

16.2 Failure-Time Distribution

16.3 The Exponential Model in Life Testing

16.4 The Weibull Model in Life Testing

Appendix A Bibliography

Appendix B Statistical Tables

Appendix C Using the R Software Program

Appendix D Answers to Odd-Numbered Exercises