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

✍ Scribed by Dharmaraja Selvamuthu, Dipayan Das.

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 623
• Category: Library

✦ Synopsis

This revised book provides an accessible presentation of concepts from probability theory, statistical methods, the design of experiments, and statistical quality control. It is shaped by the experience of the two teachers teaching statistical methods and concepts to engineering students. Practical examples and end-of-chapter exercises are the highlights of the text, as they are purposely selected from different fields. Statistical principles discussed in the book have a great relevance in several disciplines like economics, commerce, engineering, medicine, health care, agriculture, biochemistry, and textiles to mention a few. Organised into 16 chapters, the revised book discusses four major topics—probability theory, statistical methods, the design of experiments, and statistical quality control. A large number of students with varied disciplinary backgrounds need a course in basics of statistics, the design of experiments and statistical quality control at an introductory level to pursue their discipline of interest. No previous knowledge of probability or statistics is assumed, but an understanding of calculus is a prerequisite. The whole book also serves as a master level introductory course in all the three topics, as required in textile engineering or industrial engineering.

✦ Table of Contents

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