The first statistics guide focussing on practical application to process control design and maintenanceStatistics for Process Control Engineers is the only guide to statistics written by and for process control professionals. It takes a wholly practical approach to the subject. Statistics are applied throughout the life of a process control scheme - from assessing its economic benefit, designing inferential properties, identifying dynamic models, monitoring performance and diagnosing faults. This book addresses all of these areas and more.The book begins with an overview of various statistical applications in the field of process control, followed by discussions of data characteristics, probability functions, data presentation, sample size, significance testing and commonly used mathematical functions. It then shows how to select and fit a distribution to data, before moving on to the application of regression analysis and data reconciliation. The book is extensively illustrated throughout with line drawings, tables and equations, and features numerous worked examples. In addition, two appendices include the data used in the examples and an exhaustive catalogue of statistical distributions. The data and a simple-to-use software tool are available for download. The reader can thus reproduce all of the examples and then extend the same statistical techniques to real problems.* Takes a back-to-basics approach with a focus on techniques that have immediate, practical, problem-solving applications for practicing engineers, as well as engineering students* Shows how to avoid the many common errors made by the industry in applying statistics to process control* Describes not only the well-known statistical distributions but also demonstrates the advantages of applying the large number that are less well-known* Inspires engineers to identify new applications of statistical techniques to the design and support of control schemes* Provides a deeper understanding of services and products which control engineers are often tasked with assessingThis book is a valuable professional resource for engineers working in the global process industry and engineering companies, as well as students of engineering. It will be of great interest to those in the oil and gas, chemical, pulp and paper, water purification, pharmaceuticals and power generation industries, as well as for design engineers, instrument engineers and process technical support.

Preface xiiiAbout the Author xixSupplementary Material xxiPart 1: The Basics 11. Introduction 32. Application to Process Control 52.1 Benefit Estimation 52.2 Inferential Properties 72.3 Controller Performance Monitoring 72.4 Event Analysis 82.5 Time Series Analysis 93. Process Examples 113.1 Debutaniser 113.2 De-ethaniser 113.3 LPG Splitter 123.4 Propane Cargoes 173.5 Diesel Quality 173.6 Fuel Gas Heating Value 183.7 Stock Level 193.8 Batch Blending 224. Characteristics of Data 234.1 Data Types 234.2 Memory 244.3 Use of Historical Data 244.4 Central Value 254.5 Dispersion 324.6 Mode 334.7 Standard Deviation 354.8 Skewness and Kurtosis 374.9 Correlation 464.10 Data Conditioning 475. Probability Density Function 515.1 Uniform Distribution 555.2 Triangular Distribution 575.3 Normal Distribution 595.4 Bivariate Normal Distribution 625.5 Central Limit Theorem 655.6 Generating a Normal Distribution 695.7 Quantile Function 705.8 Location and Scale 715.9 Mixture Distribution 735.10 Combined Distribution 735.11 Compound Distribution 755.12 Generalised Distribution 755.13 Inverse Distribution 765.14 Transformed Distribution 765.15 Truncated Distribution 775.16 Rectified Distribution 785.17 Noncentral Distribution 785.18 Odds 795.19 Entropy 806. Presenting the Data 836.1 Box and Whisker Diagram 836.2 Histogram 846.3 Kernel Density Estimation 906.4 Circular Plots 956.5 Parallel Coordinates 976.6 Pie Chart 986.7 Quantile Plot 987. Sample Size 1057.1 Mean 1057.2 Standard Deviation 1067.3 Skewness and Kurtosis 1077.4 Dichotomous Data 1087.5 Bootstrapping 1108. Significance Testing 1138.1 Null Hypothesis 1138.2 Confidence Interval 1168.3 Six-Sigma 1188.4 Outliers 1198.5 Repeatability 1208.6 Reproducibility 1218.7 Accuracy 1228.8 Instrumentation Error 1239. Fitting a Distribution 1279.1 Accuracy of Mean and Standard Deviation 1309.2 Fitting a CDF 1319.3 Fitting a QF 1349.4 Fitting a PDF 1359.5 Fitting to a Histogram 1389.6 Choice of Penalty Function 14110. Distribution of Dependent Variables 14710.1 Addition and Subtraction 14710.2 Division and Multiplication 14810.3 Reciprocal 15310.4 Logarithmic and Exponential Functions 15310.5 Root Mean Square 16210.6 Trigonometric Functions 16411. Commonly Used Functions 16511.1 Euler's Number 16511.2 Euler-Mascheroni Constant 16611.3 Logit Function 16611.4 Logistic Function 16711.5 Gamma Function 16811.6 Beta Function 17411.7 Pochhammer Symbol 17411.8 Bessel Function 17611.9 Marcum Q-Function 17811.10 Riemann Zeta Function 18011.11 Harmonic Number 18011.12 Stirling Approximation 18211.13 Derivatives 18312. Selected Distributions 18512.1 Lognormal 18612.2 Burr 18912.3 Beta 19112.4 Hosking 19512.5 Student t 20412.6 Fisher 20812.7 Exponential 21012.8 Weibull 21312.9 Chi-Squared 21612.10 Gamma 22112.11 Binomial 22512.12 Poisson 23113. Extreme Value Analysis 23514. Hazard Function 24515. CUSUM 25316. Regression Analysis 25916.1 F Test 27516.2 Adjusted R2 27816.3 Akaike Information Criterion 27916.4 Artificial Neural Networks 28116.5 Performance Index 28617. Autocorrelation 29118. Data Reconciliation 29919. Fourier Transform 305Part 2: Catalogue of Distributions 31520. Normal Distribution 31720.1 Skew-Normal 31720.2 Gibrat 32020.3 Power Lognormal 32020.4 Logit-Normal 32120.5 Folded Normal 32120.6 Lévy 32320.7 Inverse Gaussian 32520.8 Generalised Inverse Gaussian 32920.9 Normal Inverse Gaussian 33020.10 Reciprocal Inverse Gaussian 33220.11 Q-Gaussian 33420.12 Generalised Normal 33820.13 Exponentially Modified Gaussian 34520.14 Moyal 34721. Burr Distribution 34921.1 Type I 34921.2 Type II 34921.3 Type III 34921.4 Type IV 35021.5 Type V 35121.6 Type VI 35121.7 Type VII 35321.8 Type VIII 35421.9 Type IX 35421.10 Type X 35521.11 Type XI 35621.12 Type XII 35621.13 Inverse 35722. Logistic Distribution 36122.1 Logistic 36122.2 Half-Logistic 36422.3 Skew-Logistic 36522.4 Log-Logistic 36722.5 Paralogistic 36922.6 Inverse Paralogistic 37022.7 Generalised Logistic 37122.8 Generalised Log-Logistic 37522.9 Exponentiated Kumaraswamy-Dagum 37623. Pareto Distribution 37723.1 Pareto Type I 37723.2 Bounded Pareto Type I 37823.3 Pareto Type II 37923.4 Lomax 38123.5 Inverse Pareto 38123.6 Pareto Type III 38223.7 Pareto Type IV 38323.8 Generalised Pareto 38323.9 Pareto Principle 38524. Stoppa Distribution 38924.1 Type I 38924.2 Type II 38924.3 Type III 39124.4 Type IV 39124.5 Type V 39225. Beta Distribution 39325.1 Arcsine 39325.2 Wigner Semicircle 39425.3 Balding-Nichols 39525.4 Generalised Beta 39625.5 Beta Type II 39625.6 Generalised Beta Prime 39925.7 Beta Type IV 40025.8 PERT 40125.9 Beta Rectangular 40325.10 Kumaraswamy 40425.11 Noncentral Beta 40726. Johnson Distribution 40926.1 SN 40926.2 SU 41026.3 SL 41226.4 SB 41226.5 Summary 41327. Pearson Distribution 41527.1 Type I 41627.2 Type II 41627.3 Type III 41727.4 Type IV 41827.5 Type V 42427.6 Type VI 42527.7 Type VII 42927.8 Type VIII 43327.9 Type IX 43327.10 Type X 43327.11 Type XI 43427.12 Type XII 43428. Exponential Distribution 43528.1 Generalised Exponential 43528.2 Gompertz-Verhulst 43528.3 Hyperexponential 43628.4 Hypoexponential 43728.5 Double Exponential 43828.6 Inverse Exponential 43928.7 Maxwell-Jüttner 43928.8 Stretched Exponential 44028.9 Exponential Logarithmic 44128.10 Logistic Exponential 44228.11 Q-Exponential 44228.12 Benktander 44529. Weibull Distribution 44729.1 Nukiyama-Tanasawa 44729.2 Q-Weibull 44730. Chi Distribution 45130.1 Half-Normal 45130.2 Rayleigh 45230.3 Inverse Rayleigh 45430.4 Maxwell 45430.5 Inverse Chi 45830.6 Inverse Chi-Squared 45930.7 Noncentral Chi-Squared 46031. Gamma Distribution 46331.1 Inverse Gamma 46331.2 Log-Gamma 46331.3 Generalised Gamma 46731.4 Q-Gamma 46832. Symmetrical Distributions 47132.1 Anglit 47132.2 Bates 47232.3 Irwin-Hall 47332.4 Hyperbolic Secant 47532.5 Arctangent 47632.6 Kappa 47732.7 Laplace 47832.8 Raised Cosine 47932.9 Cardioid 48132.10 Slash 48132.11 Tukey Lambda 48332.12 Von Mises 48633. Asymmetrical Distributions 48733.1 Benini 48733.2 Birnbaum-Saunders 48833.3 Bradford 49033.4 Champernowne 49133.5 Davis 49233.6 Fréchet 49433.7 Gompertz 49633.8 Shifted Gompertz 49733.9 Gompertz-Makeham 49833.10 Gamma-Gompertz 49933.11 Hyperbolic 49933.12 Asymmetric Laplace 50233.13 Log-Laplace 50433.14 Lindley 50633.15 Lindley-Geometric 50733.16 Generalised Lindley 50933.17 Mielke 50933.18 Muth 51033.19 Nakagami 51233.20 Power 51333.21 Two-Sided Power 51433.22 Exponential Power 51633.23 Rician 51733.24 Topp-Leone 51733.25 Generalised Tukey Lambda 51933.26 Wakeby 52134. Amoroso Distribution 52535. Binomial Distribution 52935.1 Negative-Binomial 52935.2 Pulya 53135.3 Geometric 53135.4 Beta-Geometric 53535.5 Yule-Simon 53635.6 Beta-Binomial 53835.7 Beta-Negative Binomial 54035.8 Beta-Pascal 54135.9 Gamma-Poisson 54235.10 Conway-Maxwell-Poisson 54335.11 Skellam 54636. Other Discrete Distributions 54936.1 Benford 54936.2 Borel-Tanner 55236.3 Consul 55536.4 Delaporte 55636.5 Flory-Schulz 55836.6 Hypergeometric 55936.7 Negative Hypergeometric 56136.8 Logarithmic 56136.9 Discrete Weibull 56336.10 Zeta 56436.11 Zipf 56536.12 Parabolic Fractal 567Appendix 1 Data Used in Examples 569Appendix 2 Summary of Distributions 577References 591Index 593