Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control

Foreword for the Second Edition
Foreword for the First Edition
Preface for the Second Edition
Preface for the First Edition
Contents
About the Authors
Acronyms
Mathematical Notations
1 Introduction
	1.1 A Brief Introduction to the Book
	1.2 Probability
		1.2.1 History
	1.3 Statistical Methods
		1.3.1 Problem of Data Representation
		1.3.2 Problem of Fitting the Distribution to the Data
		1.3.3 Problem of Estimation of Parameters
		1.3.4 Problem of Testing of Hypothesis
		1.3.5 Problem of Correlation and Regression
	1.4 Design of Experiments
		1.4.1 History
		1.4.2 Necessity
		1.4.3 Applications
	1.5 Statistical Quality Control
	References
Part I Probability
2 Basic Concepts of Probability
	2.1 Basics of Probability
	2.2 Definition of Probability
	2.3 Conditional Probability
	2.4 Total Probability Rule
	2.5 Bayes' Theorem
	2.6 Problems
	References
3 Random Variables and Expectations
	3.1 Random Variable
		3.1.1 Discrete Type Random Variable
		3.1.2 Continuous Type Random Variable
		3.1.3 Mixed Type of Random Variable
		3.1.4 Function of a Random Variable
	3.2 Moments
		3.2.1 Mean
		3.2.2 Variance
		3.2.3 Moment of Order nn
	3.3 Generating Functions
		3.3.1 Probability Generating Function
		3.3.2 Moment Generating Function
		3.3.3 Characteristic Function
	3.4 Problems
	References
4 Standard Distributions
	4.1 Standard Discrete Distributions
		4.1.1 Bernoulli, Binomial, and Geometric Distributions
		4.1.2 Poisson Distribution
		4.1.3 Discrete Uniform Distribution
		4.1.4 Hypergeometric Distribution
	4.2 Standard Continuous Distributions
		4.2.1 Uniform Distribution
		4.2.2 Normal Distribution
		4.2.3 Exponential, Gamma, and Beta Distributions
		4.2.4 Weibull, Pareto, and Rayleigh Distributions
	4.3 Problems
	References
5 Multiple Random Variables and Joint Distributions
	5.1 Two-Dimensional Random Variables
		5.1.1 Discrete Random Variables
		5.1.2 Continuous Random Variables
	5.2 Independent Random Variables
	5.3 Higher Dimensional Random Variables
	5.4 Functions of Random Variables
		5.4.1 Order Statistics
	5.5 Moments of Multivariate Distributions
		5.5.1 Variance–Covariance Matrix
		5.5.2 Correlation Coefficient
	5.6 Generating Functions
	5.7 Conditional Distribution
	5.8 Conditional Expectation and Conditional Variance
	5.9 Problems
	References
6 Limiting Distributions
	6.1 Inequalities
		6.1.1 Markov's Inequality
		6.1.2 Chebyshev's Inequality
		6.1.3 Inequality with Higher Order Moments
	6.2 Modes of Convergence
		6.2.1 Convergence in Probability
		6.2.2 Convergence in Distribution
		6.2.3 Convergence in Moment of Order rr
		6.2.4 Almost Sure Convergence
	6.3 The Weak Law of Large Numbers
	6.4 The Strong Law of Large Numbers
	6.5 Central Limit Theorem
	6.6 Problems
	References
Part II Statistical Methods
7 Descriptive Statistics
	7.1 Introduction
	7.2 Data, Information, and Description
		7.2.1 Types of Data
		7.2.2 Data, Information, and Statistic
		7.2.3 Frequency Tables
		7.2.4 Graphical Representations of Data
	7.3 Descriptive Measures
		7.3.1 Central Tendency Measures
		7.3.2 Variability Measures
		7.3.3 Coefficient of Variation
		7.3.4 Displaying the Measures and Preparing Reports
	7.4 Problems
	Reference
8 Sampling Distributions
	8.1 Introduction
	8.2 Standard Sampling Distributions
		8.2.1 Chi-Square Distribution
		8.2.2 Student's tt-Distribution
		8.2.3 upper FF-Distribution
	8.3 Sampling Distribution
		8.3.1 Sample Mean
		8.3.2 Sample Variance
		8.3.3 Empirical Distribution
		8.3.4 Order Statistics
	8.4 Some Important Results on Sampling Distributions
	8.5 Problems
	References
9 Estimation
	9.1 Point Estimation
		9.1.1 Definition of Point Estimators
		9.1.2 Properties of Estimators
		9.1.3 Cramér Rao Inequality
	9.2 Methods of Point Estimation
		9.2.1 Method of Moments
		9.2.2 Method of Maximum Likelihood
		9.2.3 Bayesian Method
		9.2.4 Asymptotic Distribution of MLEs
	9.3 Interval Estimation
		9.3.1 Confidence Interval
	9.4 Problems
	References
10 Testing of Hypothesis
	10.1 Testing of Statistical Hypothesis
		10.1.1 Null and Alternate Hypothesis
		10.1.2 Neyman–Pearson Theory
		10.1.3 Likelihood Ratio Test
		10.1.4 Test for the Population Mean
		10.1.5 Test for the Variance
		10.1.6 Test for the Distribution
		10.1.7 Testing Regarding Contingency Tables
		10.1.8 Test Regarding Proportions
	10.2 Nonparametric Statistical Tests
		10.2.1 Sign Test
		10.2.2 Median Test
		10.2.3 Kolmogorov Smirnov Test
		10.2.4 Mann–Whitney Wilcoxon U Test
	10.3 Analysis of Variance
	10.4 Problems
	References
11 Analysis of Correlation and Regression
	11.1 Introduction
	11.2 Correlation
		11.2.1 Causality
		11.2.2 Rank Correlation
	11.3 Multiple Correlation
		11.3.1 Partial Correlation
	11.4 Regression
		11.4.1 Least Squares Method
		11.4.2 Unbiased Estimator Method
		11.4.3 Hypothesis Testing Regarding Regression Parameters
		11.4.4 Confidence Interval for beta 1β1
		11.4.5 Regression to the Mean
		11.4.6 Inferences Covering beta 0β0
		11.4.7 Inferences Concerning the Mean Response of beta 0 plus beta 1 x 0β0 + β1 x0
	11.5 Logistic Regression
		11.5.1 Estimates of aa and bb
	11.6 Problems
	References
Part III Design of Experiments
12 Single-Factor Experimental Design
	12.1 Introduction
	12.2 Completely Randomized Design
		12.2.1 A Practical Problem
		12.2.2 Data Visualization
		12.2.3 Descriptive Model
		12.2.4 Test of Hypothesis
		12.2.5 Multiple Comparison Among Treatment Means (Tukey's Test)
	12.3 Randomized Block Design
		12.3.1 A Practical Problem
		12.3.2 Data Visualization
		12.3.3 Descriptive Model
		12.3.4 Test of Hypothesis
		12.3.5 Multiple Comparison Among Treatment Means
	12.4 Latin Square Design
		12.4.1 A Practical Problem
		12.4.2 Data Visualization
		12.4.3 Descriptive Model
		12.4.4 Test of Hypothesis
		12.4.5 Multiple Comparison Among Treatment Means
	12.5 Balanced Incomplete Block Design
		12.5.1 A Practical Problem
		12.5.2 Experimental Data
		12.5.3 Descriptive Model
		12.5.4 Test of Hypothesis
	12.6 Problems
	Reference
13 Multifactor Experimental Designs
	13.1 Introduction
	13.2 Two-Factor Factorial Design
		13.2.1 A Practical Problem
		13.2.2 Descriptive Model
		13.2.3 Test of Hypothesis
		13.2.4 Multiple Comparison Among Treatment Means
	13.3 Three-Factor Factorial Design
		13.3.1 A Practical Problem
		13.3.2 Descriptive Model
		13.3.3 Test of Hypothesis
	13.4 2 squared22 Factorial Design
		13.4.1 Display of 2 squared22 Factorial Design
		13.4.2 Analysis of Effects in 2 squared22 Factorial Design
		13.4.3 A Practical Problem
		13.4.4 Regression Model
		13.4.5 Response Surface
	13.5 2 cubed23 Factorial Design
		13.5.1 Display of 2 cubed23 Factorial Design
		13.5.2 Analysis of Effects in 2 cubed23 Factorial Design
		13.5.3 Yates' Algorithm
		13.5.4 A Practical Example
	13.6 Blocking and Confounding
		13.6.1 Replicates as Blocks
		13.6.2 Confounding
		13.6.3 A Practical Example
	13.7 Two-Level Fractional Factorial Design
		13.7.1 Creation of 2 Superscript 3 minus 123-1 Factorial Design
		13.7.2 Analysis of Effects in 2 Superscript 3 minus 123-1 Factorial Design with upper I equals upper A upper B upper CI=ABC
		13.7.3 Creation of Another 2 Superscript 3 minus 123-1 Factorial Design with upper I equals minus upper A upper B upper CI=-ABC
		13.7.4 Analysis of Effects in 2 Superscript 3 minus 123-1 Factorial Design with upper I equals minus upper A upper B upper CI=-ABC
		13.7.5 A Practical Example of 2 Superscript 3 minus 123-1 Factorial Design
		13.7.6 A Practical Example of 2 Superscript 4 minus 124-1 Factorial Design
		13.7.7 Design Resolution
	13.8 Problems
	Reference
14 Response Surface Methodology
	14.1 Introduction
	14.2 Response Surface Models
	14.3 Multiple Linear Regression
		14.3.1 A Generalized Model
		14.3.2 Estimation of Coefficients: Least Square Method
		14.3.3 Estimation of Variance sigma squaredσ2 of Error Term
		14.3.4 Point Estimate of Coefficients
		14.3.5 Hypothesis Test for Significance of Regression
		14.3.6 Hypothesis Test on Individual Regression Coefficient
		14.3.7 Interval Estimates of Regression Coefficients
		14.3.8 Point Estimation of Mean
		14.3.9 Adequacy of Regression Model
	14.4 Analysis of First-Order Model
	14.5 Analysis of Second-Order Model
		14.5.1 Location of Stationary Point
		14.5.2 Nature of Stationary Point
	14.6 Response Surface Designs
		14.6.1 Designs for Fitting First-Order Model
		14.6.2 Experimental Designs for Fitting Second-Order Model
	14.7 Multifactor Optimization
	14.8 Problems
	References
Part IV Statistical Quality Control
15 Acceptance Sampling
	15.1 Introduction
	15.2 Acceptance Sampling
	15.3 Single Sampling Plan for Attributes
		15.3.1 Definition of a Single Sampling Plan
		15.3.2 Operating Characteristic Curve
		15.3.3 Acceptable Quality Level
		15.3.4 Rejectable Quality Level
		15.3.5 Designing an Acceptance Sampling Plan
		15.3.6 Effect of Sample Size on OC Curve
		15.3.7 Effect of Acceptance Number on OC Curve
	15.4 Double Sampling Plan for Attributes
	15.5 Sequential Sampling Plan for Attributes
	15.6  Rectifying Sampling Plans for Attributes
	15.7 Acceptance Sampling of Variables
		15.7.1 Acceptance Sampling Plan
		15.7.2 The Producer's Risk Condition
		15.7.3 The Consumer's Risk Condition
		15.7.4 Designing of Acceptance Sampling Plan
	15.8 Problems
	Reference
16 Control Charts
	16.1 Introduction
	16.2 Control Charts
		16.2.1 Basis of Control Charts
		16.2.2 Major Parts of a Control Chart
		16.2.3 Statistical Basis for Choosing kk Equal to 3
		16.2.4 Analysis of Control Chart
	16.3 Types of Shewhart Control Charts
		16.3.1 The Mean Chart
		16.3.2 The Range Chart
		16.3.3 The Standard Deviation Chart (s-Chart)
	16.4 Process Capability Analysis
	16.5 Control Chart for Fraction Defectives
	16.6 Control Chart for the Number of Defectives
	16.7 Control Chart for the Number of Defects
	16.8 CUSUM Control Chart
	16.9 Exponentially Weighted Moving Average Control Chart
		16.9.1 Basics of EWMA
		16.9.2 Construction of EWMA Control Chart
		16.9.3 Choice of upper LL and lamdaλ
	16.10 Problems
	References
Appendix A Statistical Tables
Index