O'Reilly logo

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Statistics for Process Control Engineers

Book Description

The first statistics guide focussing on practical application to process control design and maintenance

Statistics 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 assessing

This 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. 

Table of Contents

  1. Cover
  2. Title Page
  3. Preface
  4. About the Author
  5. Supplementary Material
  6. Part 1: The Basics
    1. 1 Introduction
    2. 2 Application to Process Control
      1. 2.1 Benefit Estimation
      2. 2.2 Inferential Properties
      3. 2.3 Controller Performance Monitoring
      4. 2.4 Event Analysis
      5. 2.5 Time Series Analysis
    3. 3 Process Examples
      1. 3.1 Debutaniser
      2. 3.2 De‐ethaniser
      3. 3.3 LPG Splitter
      4. 3.4 Propane Cargoes
      5. 3.5 Diesel Quality
      6. 3.6 Fuel Gas Heating Value
      7. 3.7 Stock Level
      8. 3.8 Batch Blending
    4. 4 Characteristics of Data
      1. 4.1 Data Types
      2. 4.2 Memory
      3. 4.3 Use of Historical Data
      4. 4.4 Central Value
      5. 4.5 Dispersion
      6. 4.6 Mode
      7. 4.7 Standard Deviation
      8. 4.8 Skewness and Kurtosis
      9. 4.9 Correlation
      10. 4.10 Data Conditioning
    5. 5 Probability Density Function
      1. 5.1 Uniform Distribution
      2. 5.2 Triangular Distribution
      3. 5.3 Normal Distribution
      4. 5.4 Bivariate Normal Distribution
      5. 5.5 Central Limit Theorem
      6. 5.6 Generating a Normal Distribution
      7. 5.7 Quantile Function
      8. 5.8 Location and Scale
      9. 5.9 Mixture Distribution
      10. 5.10 Combined Distribution
      11. 5.11 Compound Distribution
      12. 5.12 Generalised Distribution
      13. 5.13 Inverse Distribution
      14. 5.14 Transformed Distribution
      15. 5.15 Truncated Distribution
      16. 5.16 Rectified Distribution
      17. 5.17 Noncentral Distribution
      18. 5.18 Odds
      19. 5.19 Entropy
    6. 6 Presenting the Data
      1. 6.1 Box and Whisker Diagram
      2. 6.2 Histogram
      3. 6.3 Kernel Density Estimation
      4. 6.4 Circular Plots
      5. 6.5 Parallel Coordinates
      6. 6.6 Pie Chart
      7. 6.7 Quantile Plot
    7. 7 Sample Size
      1. 7.1 Mean
      2. 7.2 Standard Deviation
      3. 7.3 Skewness and Kurtosis
      4. 7.4 Dichotomous Data
      5. 7.5 Bootstrapping
    8. 8 Significance Testing
      1. 8.1 Null Hypothesis
      2. 8.2 Confidence Interval
      3. 8.3 Six‐Sigma
      4. 8.4 Outliers
      5. 8.5 Repeatability
      6. 8.6 Reproducibility
      7. 8.7 Accuracy
      8. 8.8 Instrumentation Error
    9. 9 Fitting a Distribution
      1. 9.1 Accuracy of Mean and Standard Deviation
      2. 9.2 Fitting a CDF
      3. 9.3 Fitting a QF
      4. 9.4 Fitting a PDF
      5. 9.5 Fitting to a Histogram
      6. 9.6 Choice of Penalty Function
    10. 10 Distribution of Dependent Variables
      1. 10.1 Addition and Subtraction
      2. 10.2 Division and Multiplication
      3. 10.3 Reciprocal
      4. 10.4 Logarithmic and Exponential Functions
      5. 10.5 Root Mean Square
      6. 10.6 Trigonometric Functions
    11. 11 Commonly Used Functions
      1. 11.1 Euler’s Number
      2. 11.2 Euler–Mascheroni Constant
      3. 11.3 Logit Function
      4. 11.4 Logistic Function
      5. 11.5 Gamma Function
      6. 11.6 Beta Function
      7. 11.7 Pochhammer Symbol
      8. 11.8 Bessel Function
      9. 11.9 Marcum Q‐Function
      10. 11.10 Riemann Zeta Function
      11. 11.11 Harmonic Number
      12. 11.12 Stirling Approximation
      13. 11.13 Derivatives
    12. 12 Selected Distributions
      1. 12.1 Lognormal
      2. 12.2 Burr
      3. 12.3 Beta
      4. 12.4 Hosking
      5. 12.5 Student t
      6. 12.6 Fisher
      7. 12.7 Exponential
      8. 12.8 Weibull
      9. 12.9 Chi‐Squared
      10. 12.10 Gamma
      11. 12.11 Binomial
      12. 12.12 Poisson
    13. 13 Extreme Value Analysis
    14. 14 Hazard Function
    15. 15 CUSUM
    16. 16 Regression Analysis
      1. 16.1 F Test
      2. 16.2 Adjusted R
      3. 16.3 Akaike Information Criterion
      4. 16.4 Artificial Neural Networks
      5. 16.5 Performance Index
    17. 17 Autocorrelation
    18. 18 Data Reconciliation
    19. 19 Fourier Transform
  7. Part 2: Catalogue of Distributions
    1. 20 Normal Distribution
      1. 20.1 Skew‐Normal
      2. 20.2 Gibrat
      3. 20.3 Power Lognormal
      4. 20.4 Logit‐Normal
      5. 20.5 Folded Normal
      6. 20.6 Lévy
      7. 20.7 Inverse Gaussian
      8. 20.8 Generalised Inverse Gaussian
      9. 20.9 Normal Inverse Gaussian
      10. 20.10 Reciprocal Inverse Gaussian
      11. 20.11 Q‐Gaussian
      12. 20.12 Generalised Normal
      13. 20.13 Exponentially Modified Gaussian
      14. 20.14 Moyal
    2. 21 Burr Distribution
      1. 21.1 Type I
      2. 21.2 Type II
      3. 21.3 Type III
      4. 21.4 Type IV
      5. 21.5 Type V
      6. 21.6 Type VI
      7. 21.7 Type VII
      8. 21.8 Type VIII
      9. 21.9 Type IX
      10. 21.10 Type X
      11. 21.11 Type XI
      12. 21.12 Type XII
      13. 21.13 Inverse
    3. 22 Logistic Distribution
      1. 22.1 Logistic
      2. 22.2 Half‐Logistic
      3. 22.3 Skew‐Logistic
      4. 22.4 Log‐Logistic
      5. 22.5 Paralogistic
      6. 22.6 Inverse Paralogistic
      7. 22.7 Generalised Logistic
      8. 22.8 Generalised Log‐Logistic
      9. 22.9 Exponentiated Kumaraswamy–Dagum
    4. Chapter 23: Pareto Distribution
      1. 23.1 Pareto Type I
      2. 23.2 Bounded Pareto Type I
      3. 23.3 Pareto Type II
      4. 23.4 Lomax
      5. 23.5 Inverse Pareto
      6. 23.6 Pareto Type III
      7. 23.7 Pareto Type IV
      8. 23.8 Generalised Pareto
      9. 23.9 Pareto Principle
    5. 24 Stoppa Distribution
      1. 24.1 Type I
      2. 24.2 Type II
      3. 24.3 Type III
      4. 24.4 Type IV
      5. 24.5 Type V
    6. 25 Beta Distribution
      1. 25.1 Arcsine
      2. 25.2 Wigner Semicircle
      3. 25.3 Balding–Nichols
      4. 25.4 Generalised Beta
      5. 25.5 Beta Type II
      6. 25.6 Generalised Beta Prime
      7. 25.7 Beta Type IV
      8. 25.8 PERT
      9. 25.9 Beta Rectangular
      10. 25.10 Kumaraswamy
      11. 25.11 Noncentral Beta
    7. 26 Johnson Distribution
      1. 26.1 SN
      2. 26.2 SU
      3. 26.3 SL
      4. 26.4 SB
      5. 26.5 Summary
    8. 27 Pearson Distribution
      1. 27.1 Type I
      2. 27.2 Type II
      3. 27.3 Type III
      4. 27.4 Type IV
      5. 27.5 Type V
      6. 27.6 Type VI
      7. 27.7 Type VII
      8. 27.8 Type VIII
      9. 27.9 Type IX
      10. 27.10 Type X
      11. 27.11 Type XI
      12. 27.12 Type XII
    9. 28 Exponential Distribution
      1. 28.1 Generalised Exponential
      2. 28.2 Gompertz–Verhulst
      3. 28.3 Hyperexponential
      4. 28.4 Hypoexponential
      5. 28.5 Double Exponential
      6. 28.6 Inverse Exponential
      7. 28.7 Maxwell–Jüttner
      8. 28.8 Stretched Exponential
      9. 28.9 Exponential Logarithmic
      10. 28.10 Logistic Exponential
      11. 28.11 Q‐Exponential
      12. 28.12 Benktander
    10. 29 Weibull Distribution
      1. 29.1 Nukiyama–Tanasawa
      2. 29.2 Q‐Weibull
    11. 30 Chi Distribution
      1. 30.1 Half‐Normal
      2. 30.2 Rayleigh
      3. 30.3 Inverse Rayleigh
      4. 30.4 Maxwell
      5. 30.5 Inverse Chi
      6. 30.6 Inverse Chi‐Squared
      7. 30.7 Noncentral Chi‐Squared
    12. 31 Gamma Distribution
      1. 31.1 Inverse Gamma
      2. 31.2 Log‐Gamma
      3. 31.3 Generalised Gamma
      4. 31.4 Q‐Gamma
    13. 32 Symmetrical Distributions
      1. 32.1 Anglit
      2. 32.2 Bates
      3. 32.3 Irwin–Hall
      4. 32.4 Hyperbolic Secant
      5. 32.5 Arctangent
      6. 32.6 Kappa
      7. 32.7 Laplace
      8. 32.8 Raised Cosine
      9. 32.9 Cardioid
      10. 32.10 Slash
      11. 32.11 Tukey Lambda
      12. 32.12 Von Mises
    14. 33 Asymmetrical Distributions
      1. 33.1 Benini
      2. 33.2 Birnbaum–Saunders
      3. 33.3 Bradford
      4. 33.4 Champernowne
      5. 33.5 Davis
      6. 33.6 Fréchet
      7. 33.7 Gompertz
      8. 33.8 Shifted Gompertz
      9. 33.9 Gompertz–Makeham
      10. 33.10 Gamma‐Gompertz
      11. 33.11 Hyperbolic
      12. 33.12 Asymmetric Laplace
      13. 33.13 Log‐Laplace
      14. 33.14 Lindley
      15. 33.15 Lindley‐Geometric
      16. 33.16 Generalised Lindley
      17. 33.17 Mielke
      18. 33.18 Muth
      19. 33.19 Nakagami
      20. 33.20 Power
      21. 33.21 Two‐Sided Power
      22. 33.22 Exponential Power
      23. 33.23 Rician
      24. 33.24 Topp–Leone
      25. 33.25 Generalised Tukey Lambda
      26. 33.26 Wakeby
    15. 34 Amoroso Distribution
    16. 35 Binomial Distribution
      1. 35.1 Negative‐Binomial
      2. 35.2 Pόlya
      3. 35.3 Geometric
      4. 35.4 Beta‐Geometric
      5. 35.5 Yule–Simon
      6. 35.6 Beta‐Binomial
      7. 35.7 Beta‐Negative Binomial
      8. 35.8 Beta‐Pascal
      9. 35.9 Gamma‐Poisson
      10. 35.10 Conway–Maxwell–Poisson
      11. 35.11 Skellam
    17. 36 Other Discrete Distributions
      1. 36.1 Benford
      2. 36.2 Borel–Tanner
      3. 36.3 Consul
      4. 36.4 Delaporte
      5. 36.5 Flory–Schulz
      6. 36.6 Hypergeometric
      7. 36.7 Negative Hypergeometric
      8. 36.8 Logarithmic
      9. 36.9 Discrete Weibull
      10. 36.10 Zeta
      11. 36.11 Zipf
      12. 36.12 Parabolic Fractal
  8. Appendix 1: Data Used in Examples
  9. Appendix 2: Summary of Distributions
  10. References
  11. Index
  12. End User License Agreement