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Statistics and Probability with Applications for Engineers and Scientists

Book Description

Introducing the tools of statistics and probability from the ground up

An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences.

Unique among books of this kind, Statistics and Probability with Applications for Engineers and Scientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab and Microsoft Office Excel to analyze various data sets. The book also features:

  • Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices

  • A clear presentation of nonparametric methods and simple and multiple linear regression methods, as well as a brief discussion on logistic regression method

  • Comprehensive guidance on the design of experiments, including randomized block designs, one- and two-way layout designs, Latin square designs, random effects and mixed effects models, factorial and fractional factorial designs, and response surface methodology

  • A companion website containing data sets for Minitab and Microsoft Office Excel, as well as JMP routines and results

Assuming no background in probability and statistics, Statistics and Probability with Applications for Engineers and Scientists features a unique, yet tried-and-true, approach that is ideal for all undergraduate students as well as statistical practitioners who analyze and illustrate real-world data in engineering and the natural sciences.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. Chapter 1: Introduction
    1. 1.1 Designed Experiment
    2. 1.2 A Survey
    3. 1.3 An Observational Study
    4. 1.4 A Set of Historical Data
    5. 1.5 A Brief Description of What Is Covered in This Book
  7. Part I
    1. Chapter 2: Describing Data Graphically and Numerically
      1. 2.1 Getting Started with Statistics
      2. 2.2 Classification of Various Types of Data
      3. 2.3 Frequency Distribution Tables for Qualitative and Quantitative Data
      4. 2.4 Graphical Description of Qualitative and Quantitative Data
      5. 2.5 Numerical Measures of Quantitative Data
      6. 2.6 Numerical Measures of Grouped Data
      7. 2.7 Measures of Relative Position
      8. 2.8 Box-Whisker Plot
      9. 2.9 Measures of Association
      10. 2.10 Case Studies
      11. 2.11 Using JMP®
    2. Chapter 3: Elements of Probability
      1. 3.1 Introduction
      2. 3.2 Random Experiments, Sample Spaces, and Events
      3. 3.3 Concepts of Probability
      4. 3.4 Techniques of Counting Sample Points
      5. 3.5 Conditional Probability
      6. 3.6 Bayes's Theorem
      7. 3.7 Introducing Random Variables
    3. Chapter 4: Discrete Random Variables and Some Important Discrete Probability Distributions
      1. 4.1 Graphical Descriptions of Discrete Distributions
      2. 4.2 Mean and Variance of a Discrete Random Variable
      3. 4.3 The Discrete Uniform Distribution
      4. 4.4 The Hypergeometric Distribution
      5. 4.5 The Bernoulli Distribution
      6. 4.6 The Binomial Distribution
      7. 4.7 The Multinomial Distribution
      8. 4.8 The Poisson Distribution
      9. 4.9 The Negative Binomial Distribution
      10. 4.10 Some Derivations and Proofs (Optional)
      11. 4.11 A Case Study
      12. 4.12 Using JMP
    4. Chapter 5: Continuous Random Variables and Some Important Continuous Probability Distributions
      1. 5.1 Continuous Random Variables
      2. 5.2 Mean and Variance of Continuous Random Variables
      3. 5.3 Chebychev's Inequality
      4. 5.4 The Uniform Distribution
      5. 5.5 The Normal Distribution
      6. 5.6 Distribution of Linear Combination of Independent Normal Variables
      7. 5.7 Approximation of the Binomial and Poisson Distribution by the Normal Distribution
      8. 5.8 A Test of Normality
      9. 5.9 Probability Models Commonly Used in Reliability Theory
      10. 5.10 A Case Study
      11. 5.11 Using JMP
    5. Chapter 6: Distribution of Functions of Random Variables
      1. 6.1 Introduction
      2. 6.2 Distribution Functions of Two Random Variables
      3. 6.3 Extension to Several Random Variables
      4. 6.4 The Moment-Generating Function Revisited
    6. Chapter 7: Sampling Distributions
      1. 7.1 Random Sampling
      2. 7.2 The Sampling Distribution of the Mean
      3. 7.3 Sampling from a Normal Population
      4. 7.4 Order Statistics
      5. 7.5 Using JMP
    7. Chapter 8: Estimation of Population Parameters
      1. 8.1 Introduction
      2. 8.2 Point Estimators for the Population Mean and Variance
      3. 8.3 Interval Estimators for the Mean μ of a Normal Population
      4. 8.4 Interval Estimators for the Difference of Means of Two Normal Populations
      5. 8.5 Interval Estimators for the Variance of a Normal Population
      6. 8.6 Interval Estimator for the Ratio of Variances of Two Normal Populations
      7. 8.7 Point and Interval Estimators for the Parameters of Binomial Populations
      8. 8.8 Determination of Sample Size
      9. 8.9 Some Supplemental Information
      10. 8.10 A Case Study
      11. 8.11 Using JMP
    8. Chapter 9: Hypothesis Testing
      1. 9.1 Introduction
      2. 9.2 Basic Concepts of Testing a Statistical Hypothesis
      3. 9.3 Tests Concerning the Mean of a Normal Population Having Known Variance
      4. 9.4 Tests Concerning the Mean of a Normal Population Having Unknown Variance
      5. 9.5 Large Sample Theory
      6. 9.6 Tests Concerning the Difference of Means of Two Populations Having Distributions with Known Variances
      7. 9.7 Tests Concerning the Difference of Means of Two Populations Having Normal Distributions with Unknown Variances
      8. 9.8 Testing Population Proportions
      9. 9.9 Tests Concerning the Variance of a Normal Population
      10. 9.10 Tests Concerning the Ratio of Variances of Two Normal Populations
      11. 9.11 Testing of Statistical Hypotheses Using Confidence Intervals
      12. 9.12 Sequential Tests of Hypotheses
      13. 9.13 Case Studies
      14. 9.14 Using JMP
  8. Part II
    1. Chapter 10: Elements of Reliability Theory
      1. 10.1 The Reliability Function
      2. 10.2 Estimation: Exponential Distribution
      3. 10.3 Hypothesis Testing: Exponential Distribution
      4. 10.4 Estimation: Weibull Distribution
      5. 10.5 Case Studies
      6. 10.6 Using JMP
    2. Chapter 11: Statistical Quality Control–Phase I Control Charts
      1. 11.1 Basic Concepts of Quality and Its Benefits
      2. 11.2 What a Process Is and Some Valuable Tools
      3. 11.3 Common and Assignable Causes
      4. 11.4 Control Charts
      5. 11.5 Control Charts for Variables
      6. 11.6 Control Charts for Attributes
      7. 11.7 Process Capability
      8. 11.8 Case Studies
      9. 11.9 Using JMP
    3. Chapter 12: Statistical Quality Control—Phase II Control Charts
      1. 12.1 Introduction
      2. 12.2 Basic Concepts of CUSUM Control Chart
      3. 12.3 Designing a CUSUM Control Chart
      4. 12.4 The Moving Average (MA) Control Chart
      5. 12.5 The Exponentially Weighted Moving Average (EWMA) Control Chart
      6. 12.6 Case Studies
      7. 12.7 Using JMP
    4. Chapter 13: Analysis of Categorical Data
      1. 13.1 Introduction
      2. 13.2 The Chi-Square Goodness-of-Fit Test
      3. 13.3 Contingency Tables
      4. 13.4 Chi-Square Test for Homogeneity
      5. 13.5 Comments on the Distribution of the Lack-of-Fit Statistics
      6. 13.6 Case Studies
    5. Chapter 14: Nonparametric Tests
      1. 14.1 Introduction
      2. 14.2 The Sign Test
      3. 14.3 Mann–Whitney (Wilcoxon) W Test for Two Samples
      4. 14.4 Runs Test
      5. 14.5 Spearman Rank Correlation
      6. 14.6 Using JMP
    6. Chapter 15: Simple Linear Regression Analysis
      1. 15.1 Introduction
      2. 15.2 Fitting the Simple Linear Regression Model
      3. 15.3 Unbiased Estimator of σ2
      4. 15.4 Further Inferences Concerning Regression Coefficients (β0, β1), E(Y), and Y
      5. 15.5 Tests of Hypotheses for β0 and β1
      6. 15.6 Analysis of Variance Approach to Simple Linear Regression Analysis
      7. 15.7 Residual Analysis
      8. 15.8 Transformations
      9. 15.9 Inference About ρ
      10. 15.10 A Case Study (Load Cell Calibration)
      11. 15.11 Using JMP
    7. Chapter 16: Multiple Linear Regression Analysis
      1. 16.1 Introduction
      2. 16.2 Multiple Linear Regression Models
      3. 16.3 Estimation of Regression Coefficients
      4. 16.4 Multiple Linear Regression Model Using Quantitative and Qualitative Predictor Variables
      5. 16.5 Standardized Regression Coefficients
      6. 16.6 Building Regression Type Prediction Models
      7. 16.7 Residual Analysis and certain criteria for model selection
      8. 16.8 Logistic Regression
      9. 16.9 Case Studies
      10. 16.10 Using JMP
    8. Chapter 17: Analysis of Variance
      1. 17.1 Introduction
      2. 17.2 The Design Models
      3. 17.3 One-Way Experimental Layouts
      4. 17.4 Randomized Complete Block Designs
      5. 17.5 Two-Way Experimental Layouts
      6. 17.6 Latin Square Designs
      7. 17.7 Random-Effects and Mixed-Effects Models
      8. 17.8 A Case Study
      9. 17.9 Using JMP
    9. Chapter 18: The 2k Factorial Designs
      1. 18.1 Introduction
      2. 18.2 The Factorial Designs
      3. 18.4 Unreplicated 2k Factorial Designs
      4. 18.5 Blocking in the 2k Factorial Design
      5. 18.6 The 2k Fractional Factorial Designs
      6. 18.7 Case Studies
      7. 18.8 Using JMP
  9. Appendices
    1. Appendix A: Statistical Tables
    2. Appendix B: Answers to Selected Problems
    3. Appendix C: Bibliography
  10. Index