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E-book: Statistics for Chemical and Process Engineers: A Modern Approach

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  • Pub. Date: 16-Oct-2015
  • Publisher: Springer International Publishing AG
  • Language: eng
  • ISBN-13: 9783319215099
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Statistics for Chemical and Process Engineers: A Modern ApproachLarger Image
  • Format: PDF+DRM
  • Pub. Date: 16-Oct-2015
  • Publisher: Springer International Publishing AG
  • Language: eng
  • ISBN-13: 9783319215099
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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 .This book shows the reader how to develop and test models, design experiments and analyse data in ways easily applicable through readily available software tools like MS Excel® and MATLAB®. Generalized methods that can be applied irrespective of the tool at hand are a key feature of the text.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 availabl

e for instructors) to confirm the correct use of numerical techniques, and templates for use in MS Excel and MATLAB can also be downloaded from extras.springer.com.With its integrative approach to system identification, regression and statistical theory, Statistics for Chemical and Process Engineers 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.

1. Introduction to Statistics and Data Visualisation.- 2. Theoretical Foundation for Statistical Analysis.- 3. Regression.- 4. Design of Experiments.- 5. Modelling Stochastic Processes with Time Series Analysis.- 6. Modelling Dynamic Processes Using System Identification Methods.- 7.- Using MATLAB® for Statistical Analysis.- 8 : Using Excel® to do Statistical Analysis.
1 Introduction to Statistics and Data Visualisation
1(30)
1.1 Basic Descriptive Statistics
3(5)
1.1.1 Measures of Central Tendency
3(1)
1.1.2 Measures of Dispersion
4(2)
1.1.3 Other Statistical Measures
6(2)
1.2 Data Visualisation
8(13)
1.2.1 Bar Charts and Histograms
9(1)
1.2.2 Pie Charts
10(1)
1.2.3 Line Charts
10(2)
1.2.4 Box-and-Whisker Plots
12(1)
1.2.5 Scatter Plots
13(1)
1.2.6 Probability Plots
13(5)
1.2.7 Tables
18(1)
1.2.8 Sparkplots
19(1)
1.2.9 Other Data Visualisation Methods
19(2)
1.3 Friction Factor Example
21(6)
1.3.1 Explanation of the Data Set
21(2)
1.3.2 Summary Statistics
23(1)
1.3.3 Data Visualisation
24(2)
1.3.4 Some Observations on the Data Set
26(1)
1.4 Further Reading
27(1)
1.5
Chapter Problems
28(3)
1.5.1 Basic Concepts
28(1)
1.5.2 Short Exercises
29(1)
1.5.3 Computational Exercises
29(2)
2 Theoretical Foundation for Statistical Analysis
31(56)
2.1 Statistical Axioms and Definitions
31(6)
2.2 Expectation Operator
37(1)
2.3 Multivariate Statistics
38(5)
2.4 Common Statistical Distributions
43(7)
2.4.1 Normal Distribution
43(2)
2.4.2 Student's t-Distribution
45(1)
2.4.3 χ2-Distribution
46(1)
2.4.4 F-Distribution
47(1)
2.4.5 Binomial Distribution
48(2)
2.4.6 Poisson Distribution
50(1)
2.5 Parameter Estimation
50(8)
2.5.1 Considerations for Parameter Estimation
51(1)
2.5.2 Methods of Parameter Estimation
52(5)
2.5.3 Remarks on Estimating the Mean, Variance, and Standard Deviation
57(1)
2.6 Central Limit Theorem
58(1)
2.7 Hypothesis Testing and Confidence Intervals
58(21)
2.7.1 Computing the Critical Value
61(1)
2.7.2 Converting Confidence Intervals
62(2)
2.7.3 Testing the Mean
64(3)
2.7.4 Testing the Variance
67(1)
2.7.5 Testing a Ratio or Proportion
68(1)
2.7.6 Testing Two Samples
69(10)
2.8 Further Reading
79(1)
2.9
Chapter Problems
79(8)
2.9.1 Basic Concepts
79(1)
2.9.2 Short Exercises
80(3)
2.9.3 Computational Exercises
83(1)
Appendix A2 A Brief Review of Set Theory and Notation
84(3)
3 Regression
87(54)
3.1 Regression Analysis Framework
87(1)
3.2 Regression Models
88(5)
3.2.1 Linear and Nonlinear Regression Functions
90(3)
3.3 Linear Regression
93(27)
3.3.1 Ordinary, Least-Squares Regression
93(6)
3.3.2 Analysis of Variance of the Regression Model
99(3)
3.3.3 Useful Formulae for Ordinary, Least-Squares Regression
102(2)
3.3.4 Computational Example Part I: Determining the Model Parameters
104(3)
3.3.5 Model Validation
107(7)
3.3.6 Computational Example Part II: Model Validation
114(2)
3.3.7 Weighted, Least-Squares Regression
116(4)
3.4 Nonlinear Regression
120(6)
3.4.1 Gauss-Newton Solution for Nonlinear Regression
121(1)
3.4.2 Useful Formulae for Nonlinear Regression
122(1)
3.4.3 Computational Example of Nonlinear Regression
123(3)
3.5 Models and Their Use
126(1)
3.6 Summative Regression Example
126(5)
3.6.1 Data and Problem Statement
127(1)
3.6.2 Solution
127(4)
3.7 Further Reading
131(1)
3.8
Chapter Problems
131(10)
3.8.1 Basic Concepts
131(1)
3.8.2 Short Exercises
132(2)
3.8.3 Computational Exercises
134(3)
Appendix A3 Nonmatrix Solutions to the Linear, Least-Squares Regression Problem
137(1)
A.1 Nonmatrix Solution for the Ordinary, Least-Squares Case
137(2)
A.2 Nonmatrix Solution for the Weighted, Least-Squares Case
139(2)
4 Design of Experiments
141(70)
4.1 Fundamentals of Design of Experiments
141(4)
4.1.1 Sensitivity
142(1)
4.1.2 Confounding and Correlation Between Parameters
142(1)
4.1.3 Blocking
143(2)
4.1.4 Randomisation
145(1)
4.2 Types of Models
145(1)
4.2.1 Model Use
145(1)
4.3 Framework for the Analysis of Experiments
146(1)
4.4 Factorial Design
147(10)
4.4.1 Factorial Design Models
147(3)
4.4.2 Factorial Analysis
150(2)
4.4.3 Selecting Influential Parameters (Effects)
152(1)
4.4.4 Projection
152(5)
4.5 Fractional Factorial Design
157(19)
4.5.1 Notation for Fractional Factorial Experiments
158(1)
4.5.2 Resolution of Fractional Factorial Experiments
158(1)
4.5.3 Confounding in Fractional Factorial Experiments
158(8)
4.5.4 Design Procedure for Fractional Factorial Experiments
166(2)
4.5.5 Analysis of Fractional Factorial Experiments
168(1)
4.5.6 Framework for the Analysis of Factorial Designs
169(7)
4.6 Blocking and Factorial Design
176(2)
4.7 Generalised Factorial Design
178(14)
4.7.1 Obtaining an Orthogonal Basis
179(1)
4.7.2 Orthogonal Bases for Different Levels
180(6)
4.7.3 Sum of Squares in Generalised Factorial Designs
186(1)
4.7.4 Detailed Mixed-Level Example
187(5)
4.8 2k Factorial Designs with Centre Point Replicates
192(6)
4.8.1 Orthogonal Basis for 2k Factorial Designs with Centre Point Replicates
193(2)
4.8.2 Factorial Design with Centre Point Example
195(3)
4.9 Response Surface Design
198(4)
4.9.1 Central Composite Design
199(2)
4.9.2 Optimal Design
201(1)
4.9.3 Response Surface Procedure
201(1)
4.10 Further Reading
202(1)
4.11
Chapter Problems
202(9)
4.11.1 Basic Concepts
202(1)
4.11.2 Short Exercises
203(2)
4.11.3 Computational Exercises
205(3)
Appendix A4 Nonmatrix Approach to the Analysis of 2k-Factorial Design Experiments
208(3)
5 Modelling Stochastic Processes with Time Series Analysis
211(72)
5.1 Fundamentals of Time Series Analysis
212(7)
5.1.1 Estimating the Autocovariance and Cross-Co variance and Correlation Functions
215(1)
5.1.2 Obtaining a Stationary Time Series
216(1)
5.1.3 Edmonton Weather Data Series Example
216(3)
5.2 Common Time Series Models
219(3)
5.3 Theoretical Examination of Time Series Models
222(18)
5.3.1 Properties of a White Noise Process
223(1)
5.3.2 Properties of a Moving-Average Process
223(5)
5.3.3 Properties of an Autoregressive Process
228(5)
5.3.4 Properties of an Integrating Process
233(2)
5.3.5 Properties of ARMA and ARIMA Processes
235(2)
5.3.6 Properties of the Seasonal Component of a Time Series Model
237(2)
5.3.7 Summary of the Theoretical Properties for Different Time Series Models
239(1)
5.4 Time Series Modelling
240(19)
5.4.1 Estimating the Time Series Model Parameters
241(4)
5.4.2 Maximum-Likelihood Parameter Estimates for ARMA Models
245(5)
5.4.3 Model Validation for Time Series Models
250(3)
5.4.4 Model Prediction and Forecasting Using Time Series Models
253(6)
5.5 Frequency-Domain Analysis of Time Series
259(7)
5.5.1 Fourier Transform
259(3)
5.5.2 Periodogram and Its Use in Frequency-Domain Analysis of Time Series
262(4)
5.6 State-Space Modelling of Time Series
266(5)
5.6.1 State-Space Model for Time Series
266(1)
5.6.2 The Kalman Equation
267(3)
5.6.3 Maximum-Likelihood State-Space Estimates
270(1)
5.7 Comprehensive Example of Time Series Modelling
271(2)
5.7.1 Summary of Available Information
271(1)
5.7.2 Obtaining the Final Univariate Model
272(1)
5.8 Further Reading
273(1)
5.9
Chapter Problems
274(9)
5.9.1 Basic Concepts
275(1)
5.9.2 Short Exercises
276(1)
5.9.3 Computational Exercises
276(1)
Appendix A5 Data Sets for This
Chapter
277(1)
A5.1 Edmonton Weather Data Series (1882--2002)
277(4)
A5.2 AR(2) Process Data
281(1)
A5.3 MA(3) Process Data
282(1)
6 Modelling Dynamic Processes Using System Identification Methods
283(54)
6.1 Control and Process System Identification
284(7)
6.1.1 Predictability of Process Models
287(4)
6.2 Framework for System Identification
291(1)
6.3 Open-Loop Process Identification
292(11)
6.3.1 Parameter Estimation in Process Identification
292(4)
6.3.2 Model Validation in Process Identification
296(2)
6.3.3 Design of Experiments in Process Identification
298(2)
6.3.4 Final Considerations in Open-Loop Process Identification
300(3)
6.4 Closed-Loop Process Identification
303(6)
6.4.1 Indirect Identification of a Closed-Loop Process
305(1)
6.4.2 Direct Identification of a Closed-Loop Process
306(2)
6.4.3 Joint Input-Output Identification of a Closed-Loop Process
308(1)
6.5 Nonlinear Process Identification
309(1)
6.5.1 Transformation of Nonlinear Models: Wiener-Hammerstein Models
310(1)
6.6 Modelling the Water Level in a Tank
310(11)
6.6.1 Design of Experiment
311(2)
6.6.2 Raw Data
313(1)
6.6.3 Linear Model Creation and Validation
314(4)
6.6.4 Nonlinear Model Creation and Validation
318(2)
6.6.5 Final Comments
320(1)
6.7 Further Reading
321(1)
6.8
Chapter Problems
321(16)
6.8.1 Basic Concepts
322(1)
6.8.2 Short Exercises
322(2)
6.8.3 Computational Exercises
324(1)
Appendix A6 Data Sets for This
Chapter
324(1)
A6.1 Water Level in Tanks 1 and 2 Data
324(13)
7 Using MATLAB® for Statistical Analysis
337(26)
7.1 Basic Statistical Functions
337(1)
7.2 Basic Functions for Creating Graphs
337(4)
7.3 The Statistics and Machine Learning Toolbox
341(3)
7.3.1 Probability Distributions
341(1)
7.3.2 Advanced Statistical Functions
341(1)
7.3.3 Useful Probability Functions
342(1)
7.3.4 Linear Regression Analysis
342(1)
7.3.5 Design of Experiments
342(2)
7.4 The System Identification Toolbox
344(2)
7.5 The Econometrics Toolbox
346(1)
7.6 The Signal Processing Toolbox
346(1)
7.7 MATLAB® Recipes
347(7)
7.7.1 Periodogram
350(1)
7.7.2 Autocorrelation Plot
351(1)
7.7.3 Correlation Plot
352(1)
7.7.4 Cross-Correlation Plot
352(2)
7.8 MATLAB® Examples
354(8)
7.8.1 Linear Regression Example in MATLAB
354(4)
7.8.2 Nonlinear Regression Example in MATLAB
358(3)
7.8.3 System Identification Example in MATLAB
361(1)
7.9 Further Reading
362(1)
8 Using Excel® to Do Statistical Analysis
363(36)
8.1 Ranges and Arrays in Excel
363(2)
8.2 Useful Excel Functions
365(1)
8.2.1 Array Functions in Excel
365(1)
8.2.2 Statistical Functions in Excel
365(1)
8.3 Excel Macros and Security
366(2)
8.3.1 Security in Excel
367(1)
8.4 The Excel Solver Add-In
368(6)
8.4.1 Installing the Solver Add-In
368(1)
8.4.2 Using the Solver Add-In
369(5)
8.5 The Excel Data Analysis Add-In
374(2)
8.6 Excel Templates
376(12)
8.6.1 Normal Probability Plot Template
377(1)
8.6.2 Box-and-Whisker Plot Template
378(5)
8.6.3 Periodogram Template
383(2)
8.6.4 Linear Regression Template
385(1)
8.6.5 Nonlinear Regression Template
386(1)
8.6.6 Factorial Design Analysis Template
386(2)
8.7 Excel Examples
388(7)
8.7.1 Linear Regression Example in Excel
389(2)
8.7.2 Nonlinear Regression Example in Excel
391(4)
8.7.3 Factorial Design Examples Using Excel
395(1)
8.8 Further Reading
395(4)
Appendix A Solution Key
399(4)
Chapter 1
399(1)
Chapter 2
399(1)
Chapter 3
400(1)
Chapter 4
401(1)
Chapter 5
401(1)
Chapter 6
401(2)
References 403(4)
Subject Index 407(6)
Index of Excel and MATLAB Topics 413
Prof. Dr. Yuri A. W. Shardt is currently the chair of the Department of Automation Engineering (DE: Fachgebiet Automatisierungstechnik) in the Faculty of Computer Science and Automation (DE: Fakultät Informatik und Automatisierung) at the Technical University of Ilmenau (DE: Technische Universität Ilmenau), working in the fields of big data, including process identification and monitoring with an emphasis on the development and industrial implementation of soft sensors; holistic control, including the development of advanced control strategies for complex industrial process; and the smart world, including such implementations as smart factories, smart home, Industry 4.0, and smart grids. Previously, he worked at the University of Waterloo in the Department of Chemical Engineering and at the University of Duisburg-Essen in the Institute of Control and Complex Systems (DE: Fachgebiet Automatisierungstechnik und komplexe Systeme, AKS) as an Alexander von Humboldt Fellow. He has written 30 papers appearing in such journals as Automatica, Journal of Process Control, IEEE Transactions on Industrial Electronics, and Industrial and Engineering Chemistry Research on topics ranging from system identification, soft sensor development, to process control. He has presented his research at numerous conferences and taught various courses in the intersection between statistics, chemical engineering, process control, EXCEL®, and MATLAB®. Prof. Dr. Shardt completed his doctoral degree under the supervision of Prof. Dr. Biao Huang at the University of Alberta. His thesis examined the methods for extracting valuable data for system identification from data historians for application to soft sensor design. In addition to his academic work, he has spent considerable time in industry working on implementing various process control solutions. He also has interests in linguistics, as well as software internationalisation and localisation.
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