Statistics for Chemical and Process Engineers: A Modern Approach

Description

A coherent, concise, and comprehensive course in the statistics needed for a modern career in chemical engineering covers all of the concepts required for the American Fundamentals of Engineering Examination. Statistics for Chemical and Process Engineers (second edition) shows the reader how to develop and test models, design experiments and analyze data in ways easily applicable through readily available software tools like MS Excel® and MATLAB® and is updated for the most recent versions of both. Generalized methods that can be applied irrespective of the tool at hand are a key feature of the text, and it now contains an introduction to the use of state-space methods. The reader is given a detailed framework for statistical procedures covering: data visualization;probability;linear and nonlinear regression; experimental design (including factorial and fractional factorial designs); and dynamic process identification. Main concepts are illustrated with chemical- and process-engineering-relevant examples that can also serve as the bases for checking any subsequent real implementations. Questions are provided (with solutions available for instructors) to confirm the correct use of numerical techniques, and templates for use in MS Excel and MATLAB are also available for download. With its integrative approach to system identification, regression, and statistical theory, this book provides an excellent means of revision and self-study for chemical and process engineers working in experimental analysis and design in petrochemicals, ceramics, oil and gas, automotive and similar industries, and invaluable instruction to advanced undergraduate and graduate students looking to begin a career in the process industries. Preface Symbols and Abbreviations Symbols Abbreviations Contents List of Figures List of Tables 1 Introduction to Statistics and Data Visualisation 1.1 Basic Descriptive Statistics 1.1.1 Measures of Central Tendency 1.1.2 Measures of Dispersion 1.1.3 Other Statistical Measures 1.2 Data Visualisation 1.2.1 Bar Charts and Histograms 1.2.2 Pie Charts 1.2.3 Line Charts 1.2.4 Box-and-Whisker Plots 1.2.5 Scatter Plots 1.2.6 Probability Plots 1.2.7 Tables 1.2.8 Sparkplots 1.2.9 Other Data Visualisation Methods 1.3 Friction Factor Example 1.3.1 Explanation of the Data Set 1.3.2 Summary Statistics 1.3.3 Data Visualisation 1.3.4 Some Observations on the Data Set 1.4 Further Reading 1.5 Chapter Problems 1.5.1 Basic Concepts 1.5.2 Short Exercises 1.5.3 Computational Exercises 2 Theoretical Foundation for Statistical Analysis 2.1 Statistical Axioms and Definitions 2.2 Expectation Operator 2.3 Multivariate Statistics 2.4 Common Statistical Distributions 2.4.1 Normal Distribution 2.4.2 Student’s t-Distribution 2.4.3 χ2-Distribution 2.4.4 F-Distribution 2.4.5 Binomial Distribution 2.4.6 Poisson Distribution 2.5 Parameter Estimation 2.5.1 Considerations for Parameter Estimation 2.5.2 Methods of Parameter Estimation 2.5.3 Remarks on Estimating the Mean, Variance, and Standard Deviation 2.6 Central Limit Theorem 2.7 Hypothesis Testing and Confidence Intervals 2.7.1 Computing the Critical Value 2.7.2 Converting Confidence Intervals 2.7.3 Testing the Mean 2.7.4 Testing the Variance 2.7.5 Testing a Ratio or Proportion 2.7.6 Testing Two Samples 2.8 Further Reading 2.9 Chapter Problems 2.9.1 Basic Concepts 2.9.2 Short Exercises 2.9.3 Computational Exercises Appendix A2: A Brief Review of Set Theory and Notation 3 Regression 3.1 Regression Analysis Framework 3.2 Regression Models 3.2.1 Linear and Nonlinear Regression Functions 3.3 Linear Regression 3.3.1 Ordinary, Least-Squares Regression 3.3.2 Analysis of Variance of the Regression Model 3.3.3 Useful, Formulae for Ordinary, Least-Squares Regression 3.3.4 Computational Example Part I: Determining the Model Parameters 3.3.5 Model Validation 3.3.6 Computational Example Part II: Model Validation 3.3.7 Weighted, Least-Squares Regression 3.4 Nonlinear Regression 3.4.1 Gauss–Newton Solution for Nonlinear Regression 3.4.2 Useful Formulae for Nonlinear Regression 3.4.3 Computational Example of Nonlinear Regression 3.5 Models and Their Use 3.6 Summative Regression Example 3.6.1 Data and Problem Statement 3.6.2 Solution 3.7 Further Reading 3.8 Chapter Problems 3.8.1 Basic Concepts 3.8.2 Short Exercises 3.8.3 Computational Exercises Appendix A3: Nonmatrix Solutions to the Linear, Least-Squares Regression Problem A3.1 Nonmatrix Solution for the Ordinary, Least-Squares Case A3.2 Nonmatrix Solution for the Weighted, Least-Squares Case 4 Design of Experiments 4.1 Fundamentals of Design of Experiments 4.1.1 Sensitivity 4.1.2 Confounding and Correlation Between Parameters 4.1.3 Blocking 4.1.4 Randomization 4.2 Types of Models 4.2.1 Model Use 4.3 Framework for the Analysis of Experiments 4.4 Factorial Design 4.4.1 Factorial Design Models 4.4.2 Factorial Analysis 4.4.3 Selecting Influential Parameters (Effects) 4.4.4 Projection 4.5 Fractional Factorial Design 4.5.1 Notation for Fractional Factorial Experiments 4.5.2 Resolution of Fractional Factorial Experiments 4.5.3 Confounding in Fractional Factorial Experiments 4.5.4 Design Procedure for Fractional Factorial Experiments 4.5.5 Analysis of Fractional Factorial Experiments 4.5.6 Framework for the Analysis of Factorial Designs 4.6 Blocking and Factorial Design 4.7 Generalized Factorial Design 4.7.1 Obtaining an Orthogonal Basis 4.7.2 Orthogonal Bases for Different Levels 4.7.3 Sum of Squares in Generalized Factorial Designs 4.7.4 Detailed Mixed-Level Example 4.8 2k-Factorial Designs with Centre Point Replicates 4.8.1 Orthogonal Basis for 2k-Factorial Designs with Centre Point Replicates 4.8.2 Factorial Design with Centre Point Example 4.9 Response Surface Design 4.9.1 Central Composite Design 4.9.2 Optimal Design 4.9.3 Response Surface Procedure 4.10 Further Reading 4.11 Chapter Problems 4.11.1 Basic Concepts 4.11.2 Short Exercises 4.11.3 Computational Exercises Appendix A4: Nonmatrix Approach to the Analysis of 2k-Factorial Design Experiments 5 Modelling Stochastic Processes with Time-Series Analysis 5.1 Fundamentals of Time-Series Analysis 5.1.1 Estimating the Auto- and Cross-Covariance and Correlation Functions 5.1.2 Obtaining a Stationary Time Series 5.1.3 Edmonton Weather Data Series Example 5.2 Common Time-Series Models 5.3 Theoretical Examination of Time-Series Models 5.3.1 Properties of a White-Noise Process 5.3.2 Properties of a Moving-Average Process 5.3.3 Properties of an Autoregressive Process 5.3.4 Properties of an Integrating Process 5.3.5 Properties of ARMA and ARIMA Processes 5.3.6 Properties of the Seasonal Component of a Time-Series Model 5.3.7 Summary of the Theoretical Properties for Different Time-Series Models 5.4 Time-Series Modelling 5.4.1 Estimating the Time-Series Model Parameters 5.4.2 Maximum Likelihood Parameter Estimates for ARMA Models 5.4.3 Model Validation for Time-Series Models 5.4.4 Model Prediction and Forecasting Using Time-Series Models 5.5 Frequency-Domain Analysis of Time Series 5.5.1 Fourier Transform 5.5.2 The Periodogram and Its Use in the Frequency-Domain Analysis of Time Series 5.6 State-Space Modelling of Time Series 5.6.1 State-Space Model for Time Series 5.6.2 The Kalman Equation 5.6.3 Maximum Likelihood State-Space Estimates 5.7 Comprehensive Example of Time-Series Modelling 5.7.1 Summary of Available Information 5.7.2 Obtaining the Final Univariate Model 5.8 Further Reading 5.9 Chapter Problems 5.9.1 Basic Concepts 5.9.2 Short Exercises 5.9.3 Computational Exercises Appendix A5: Data Sets for This Chapter A5.1: Edmonton Weather Data Series (1882–2002) A5.2: AR(2) Process Data A5.3: MA(3) Process Data 6 Modelling Dynamic Processes Using System Identification Methods 6.1 Control and Process System Identification 6.1.1 Predictability of Process Models 6.2 Framework for System Identification 6.3 Open-Loop Process Identification 6.3.1 Parameter Estimation in Process Identification 6.3.2 Model Validation in Process Identification 6.3.3 Design of Experiments in Process Identification 6.3.4 Final Considerations in Open-Loop Process Identification 6.4 Closed-Loop Process Identification 6.4.1 Indirect Identification of a Closed-Loop Process 6.4.2 Direct Identification of a Closed-Loop Process 6.4.3 Joint Input–Output Identification of a Closed-Loop Process 6.5 Nonlinear Process Identification 6.5.1 Transformation of Nonlinear Models: Wiener–Hammerstein Models 6.6 Modelling the Water Level in a Tank 6.6.1 Design of Experiment 6.6.2 Raw Data 6.6.3 Linear Model Creation and Validation 6.6.4 Nonlinear Model Creation and Validation 6.6.5 Final Comments 6.7 Further Reading 6.8 Chapter Problems 6.8.1 Basic Concepts 6.8.2 Short Exercises 6.8.3 Computational Exercises Appendix A6: Data Sets for This Chapter A6.1: Water Level in Tanks 1 and 2 Data 7 Using MATLAB® for Statistical Analysis 7.1 Basic Statistical Functions 7.2 Basic Functions for Creating Graphs 7.3 The Statistics and Machine Learning Toolbox 7.3.1 Probability Distributions 7.3.2 Advanced Statistical Functions 7.3.3 Advanced Probability Functions 7.3.4 Linear Regression Analysis 7.3.5 Design of Experiments 7.4 The System Identification Toolbox 7.5 The Econometrics Toolbox 7.6 The Signal Processing Toolbox 7.7 MATLAB® Recipes 7.7.1 Periodogram 7.7.2 Autocorrelation Plot 7.7.3 Correlation Plot 7.7.4 Cross-Correlation Plot 7.8 MATLAB® Examples 7.8.1 Linear Regression Example in MATLAB® 7.8.2 Nonlinear Regression Example in MATLAB® 7.8.3 System Identification Example in MATLAB® 7.9 Further Reading 8 Using Excel® to Do Statistical Analysis 8.1 Ranges and Arrays in Excel® 8.2 Useful Excel® Functions 8.2.1 Array Functions in Excel® 8.2.2 Statistical Functions in Excel® 8.3 Excel® Macros and Security 8.3.1 Security in Excel® 8.4 The Excel® Solver Add-In 8.4.1 Installing the Solver Add-In 8.4.2 Using the Solver Add-In 8.5 The Excel® Data Analysis Add-In 8.6 Excel® Templates 8.6.1 Normal Probability Plot Template 8.6.2 Box-and-Whisker Plot Template 8.6.3 Periodogram Template 8.6.4 Linear Regression Template 8.6.5 Nonlinear Regression Template 8.6.6 Factorial Design Analysis Template 8.7 Excel® Examples 8.7.1 Linear Regression Example in Excel® 8.7.2 Nonlinear Regression Example in Excel® 8.7.3 Factorial Design Examples Using Excel® 8.8 Further Reading Appendix A Solution Key References Index MATLAB and Excel Functions