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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
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.
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Table of Contents
Cover
Title Page
Preface
About the Author
Supplementary Material
Part 1: The Basics
1 Introduction
2 Application to Process Control
2.1 Benefit Estimation
2.2 Inferential Properties
2.3 Controller Performance Monitoring
2.4 Event Analysis
2.5 Time Series Analysis
3 Process Examples
3.1 Debutaniser
3.2 De‐ethaniser
3.3 LPG Splitter
3.4 Propane Cargoes
3.5 Diesel Quality
3.6 Fuel Gas Heating Value
3.7 Stock Level
3.8 Batch Blending
4 Characteristics of Data
4.1 Data Types
4.2 Memory
4.3 Use of Historical Data
4.4 Central Value
4.5 Dispersion
4.6 Mode
4.7 Standard Deviation
4.8 Skewness and Kurtosis
4.9 Correlation
4.10 Data Conditioning
5 Probability Density Function
5.1 Uniform Distribution
5.2 Triangular Distribution
5.3 Normal Distribution
5.4 Bivariate Normal Distribution
5.5 Central Limit Theorem
5.6 Generating a Normal Distribution
5.7 Quantile Function
5.8 Location and Scale
5.9 Mixture Distribution
5.10 Combined Distribution
5.11 Compound Distribution
5.12 Generalised Distribution
5.13 Inverse Distribution
5.14 Transformed Distribution
5.15 Truncated Distribution
5.16 Rectified Distribution
5.17 Noncentral Distribution
5.18 Odds
5.19 Entropy
6 Presenting the Data
6.1 Box and Whisker Diagram
6.2 Histogram
6.3 Kernel Density Estimation
6.4 Circular Plots
6.5 Parallel Coordinates
6.6 Pie Chart
6.7 Quantile Plot
7 Sample Size
7.1 Mean
7.2 Standard Deviation
7.3 Skewness and Kurtosis
7.4 Dichotomous Data
7.5 Bootstrapping
8 Significance Testing
8.1 Null Hypothesis
8.2 Confidence Interval
8.3 Six‐Sigma
8.4 Outliers
8.5 Repeatability
8.6 Reproducibility
8.7 Accuracy
8.8 Instrumentation Error
9 Fitting a Distribution
9.1 Accuracy of Mean and Standard Deviation
9.2 Fitting a CDF
9.3 Fitting a QF
9.4 Fitting a PDF
9.5 Fitting to a Histogram
9.6 Choice of Penalty Function
10 Distribution of Dependent Variables
10.1 Addition and Subtraction
10.2 Division and Multiplication
10.3 Reciprocal
10.4 Logarithmic and Exponential Functions
10.5 Root Mean Square
10.6 Trigonometric Functions
11 Commonly Used Functions
11.1 Euler’s Number
11.2 Euler–Mascheroni Constant
11.3 Logit Function
11.4 Logistic Function
11.5 Gamma Function
11.6 Beta Function
11.7 Pochhammer Symbol
11.8 Bessel Function
11.9 Marcum Q‐Function
11.10 Riemann Zeta Function
11.11 Harmonic Number
11.12 Stirling Approximation
11.13 Derivatives
12 Selected Distributions
12.1 Lognormal
12.2 Burr
12.3 Beta
12.4 Hosking
12.5 Student t
12.6 Fisher
12.7 Exponential
12.8 Weibull
12.9 Chi‐Squared
12.10 Gamma
12.11 Binomial
12.12 Poisson
13 Extreme Value Analysis
14 Hazard Function
15 CUSUM
16 Regression Analysis
16.1 F Test
16.2 Adjusted R
16.3 Akaike Information Criterion
16.4 Artificial Neural Networks
16.5 Performance Index
17 Autocorrelation
18 Data Reconciliation
19 Fourier Transform
Part 2: Catalogue of Distributions
20 Normal Distribution
20.1 Skew‐Normal
20.2 Gibrat
20.3 Power Lognormal
20.4 Logit‐Normal
20.5 Folded Normal
20.6 Lévy
20.7 Inverse Gaussian
20.8 Generalised Inverse Gaussian
20.9 Normal Inverse Gaussian
20.10 Reciprocal Inverse Gaussian
20.11 Q‐Gaussian
20.12 Generalised Normal
20.13 Exponentially Modified Gaussian
20.14 Moyal
21 Burr Distribution
21.1 Type I
21.2 Type II
21.3 Type III
21.4 Type IV
21.5 Type V
21.6 Type VI
21.7 Type VII
21.8 Type VIII
21.9 Type IX
21.10 Type X
21.11 Type XI
21.12 Type XII
21.13 Inverse
22 Logistic Distribution
22.1 Logistic
22.2 Half‐Logistic
22.3 Skew‐Logistic
22.4 Log‐Logistic
22.5 Paralogistic
22.6 Inverse Paralogistic
22.7 Generalised Logistic
22.8 Generalised Log‐Logistic
22.9 Exponentiated Kumaraswamy–Dagum
Chapter 23: Pareto Distribution
23.1 Pareto Type I
23.2 Bounded Pareto Type I
23.3 Pareto Type II
23.4 Lomax
23.5 Inverse Pareto
23.6 Pareto Type III
23.7 Pareto Type IV
23.8 Generalised Pareto
23.9 Pareto Principle
24 Stoppa Distribution
24.1 Type I
24.2 Type II
24.3 Type III
24.4 Type IV
24.5 Type V
25 Beta Distribution
25.1 Arcsine
25.2 Wigner Semicircle
25.3 Balding–Nichols
25.4 Generalised Beta
25.5 Beta Type II
25.6 Generalised Beta Prime
25.7 Beta Type IV
25.8 PERT
25.9 Beta Rectangular
25.10 Kumaraswamy
25.11 Noncentral Beta
26 Johnson Distribution
26.1 SN
26.2 SU
26.3 SL
26.4 SB
26.5 Summary
27 Pearson Distribution
27.1 Type I
27.2 Type II
27.3 Type III
27.4 Type IV
27.5 Type V
27.6 Type VI
27.7 Type VII
27.8 Type VIII
27.9 Type IX
27.10 Type X
27.11 Type XI
27.12 Type XII
28 Exponential Distribution
28.1 Generalised Exponential
28.2 Gompertz–Verhulst
28.3 Hyperexponential
28.4 Hypoexponential
28.5 Double Exponential
28.6 Inverse Exponential
28.7 Maxwell–Jüttner
28.8 Stretched Exponential
28.9 Exponential Logarithmic
28.10 Logistic Exponential
28.11 Q‐Exponential
28.12 Benktander
29 Weibull Distribution
29.1 Nukiyama–Tanasawa
29.2 Q‐Weibull
30 Chi Distribution
30.1 Half‐Normal
30.2 Rayleigh
30.3 Inverse Rayleigh
30.4 Maxwell
30.5 Inverse Chi
30.6 Inverse Chi‐Squared
30.7 Noncentral Chi‐Squared
31 Gamma Distribution
31.1 Inverse Gamma
31.2 Log‐Gamma
31.3 Generalised Gamma
31.4 Q‐Gamma
32 Symmetrical Distributions
32.1 Anglit
32.2 Bates
32.3 Irwin–Hall
32.4 Hyperbolic Secant
32.5 Arctangent
32.6 Kappa
32.7 Laplace
32.8 Raised Cosine
32.9 Cardioid
32.10 Slash
32.11 Tukey Lambda
32.12 Von Mises
33 Asymmetrical Distributions
33.1 Benini
33.2 Birnbaum–Saunders
33.3 Bradford
33.4 Champernowne
33.5 Davis
33.6 Fréchet
33.7 Gompertz
33.8 Shifted Gompertz
33.9 Gompertz–Makeham
33.10 Gamma‐Gompertz
33.11 Hyperbolic
33.12 Asymmetric Laplace
33.13 Log‐Laplace
33.14 Lindley
33.15 Lindley‐Geometric
33.16 Generalised Lindley
33.17 Mielke
33.18 Muth
33.19 Nakagami
33.20 Power
33.21 Two‐Sided Power
33.22 Exponential Power
33.23 Rician
33.24 Topp–Leone
33.25 Generalised Tukey Lambda
33.26 Wakeby
34 Amoroso Distribution
35 Binomial Distribution
35.1 Negative‐Binomial
35.2 Pόlya
35.3 Geometric
35.4 Beta‐Geometric
35.5 Yule–Simon
35.6 Beta‐Binomial
35.7 Beta‐Negative Binomial
35.8 Beta‐Pascal
35.9 Gamma‐Poisson
35.10 Conway–Maxwell–Poisson
35.11 Skellam
36 Other Discrete Distributions
36.1 Benford
36.2 Borel–Tanner
36.3 Consul
36.4 Delaporte
36.5 Flory–Schulz
36.6 Hypergeometric
36.7 Negative Hypergeometric
36.8 Logarithmic
36.9 Discrete Weibull
36.10 Zeta
36.11 Zipf
36.12 Parabolic Fractal
Appendix 1: Data Used in Examples
Appendix 2: Summary of Distributions
References
Index
End User License Agreement
List of Tables
Chapter 04
Table 4.1
Averaging C
4
content of propane cargoes
Table 4.2
Averaging SG of heavy fuel oil cargoes
Table 4.3
Analyses of propane cargoes
Table 4.4
Applying trapezium rule to determine moments
Chapter 09
Table 9.1
Fitting the CDF and quantile function of a normal distribution
Table 9.2
Fitting the PDF of a normal distribution
Table 9.3
Fitting a normal distribution to a histogram
Table 9.4
Kolmogorov–Smirnov test
Chapter 11
Table 11.1
Common derivatives
Chapter 12
Table 12.1
Bounds for the Hosking distribution
Table 12.2
Calculation of
μ, σ, γ
and
κ
for Hosking distribution
Table 12.3
Measured and predicted values for
y
Chapter 16
Table 16.1
LPG splitter data for development of inferential
Table 16.2
Impact of choice of penalty function
Table 16.3
Use of weighted least squares regression
Table 16.4
LPG splitter data collected over wide operating range
Chapter 17
Table 17.1
Initial estimate of coefficients
Table 17.2
Intermediate estimate of coefficients
Table 17.3
Final estimate of coefficients
Chapter 26
Table 26.1
Results of fitting Johnson distributions to C
4
data
Chapter 34
Table 34.1 Distributions represented by the Amoroso distribution
Appendix 01
Table A1.1
Results for vol% C
4
in propane rundown
Table A1.2
Results for vol% C
2
in 100 propane cargoes
Table A1.3
Gasoil 95% distillation points (°C)
Table A1.4
Results for fuel gas NHV (MJ/sm
3
)
Table A1.5
Fuel gas analyses (mol %)
Table A1.6
Stock levels
Table A1.7
Results for batch blending (including trim blends)
Table A1.8
Two‐tailed confidence intervals
Table A1.9
One‐tailed confidence intervals
Appendix 02
Table A2.1
Summary of continuous distributions
Table A2.2
Summary of discrete distributions
List of Illustrations
Chapter 02
Figure 2.1
Same percentage rule
Figure 2.2
Properly fitting a distribution
Chapter 03
Figure 3.1
Variation in LPG splitter reflux
Figure 3.2
Distribution of reflux flow
Figure 3.3
Distribution of high reflux events
Figure 3.4
Distribution of intervals between reflux events
Figure 3.5
Laboratory results for C
4
content of propane
Figure 3.6
Skewed distribution of C
4
results
Figure 3.7
Changes in C
4
content
Figure 3.8
Comparison between analyser and inferential
Figure 3.9
Scatter plot of inferential against analyser
Figure 3.10
Actual distribution very different from normal
Figure 3.11
Laboratory results for gasoil 95% distillation point
Figure 3.12
Variation in site’s fuel gas heating value
Figure 3.13
Disturbances to heating value
Figure 3.14
Small tails compared to normal distribution
Figure 3.15
Variation in stock level
Figure 3.16
Skewed distribution of stock levels
Figure 3.17
Variation in blend property
Chapter 04
Figure 4.1
Centroid of propane composition
Figure 4.2
Multimodal distributions
Figure 4.3
Skewness
Figure 4.4
Increasing kurtosis
Figure 4.5
Decreasing variance
Figure 4.6
Comparison between kurtosis and variance
Figure 4.7
Normal distribution
Figure 4.8
Convergence of calculations of moments
Chapter 05
Figure 5.1
Expected frequency of total score from two dice
Figure 5.2
Expected distribution
Figure 5.3
Cumulative probability
Figure 5.4
Examples of PDF
Figure 5.5
Examples of CDF
Figure 5.6
Development of the triangular distribution
Figure 5.7
PDF of continuous triangular distribution
Figure 5.8
CDF of continuous triangular distribution
Figure 5.9
Effect of varying
μ
and
σ
on PDF of normal distribution
Figure 5.10
Error function
Figure 5.11
Effect of varying
μ
and
σ
on CDF of normal distribution
Figure 5.12
Plot of bivariate PDF
Figure 5.13
Effect of CH
4
content on distribution of H
2
content
Figure 5.14
Effect of H
2
content on distribution of CH
4
content
Figure 5.15
Plot of bivariate CDF
Figure 5.16
Frequency distribution of the score from a single dice
Figure 5.17
Frequency distribution of the total score from two dice
Figure 5.18
Frequency distribution of the total score from five dice
Figure 5.19
Frequency distribution of the score from a single modified dice
Figure 5.20
Frequency distribution of the total score from seven modified dice
Figure 5.21
Probability distribution of the product of three dice throws
Figure 5.22
Probability distribution of the logarithm of the product of three dice throws
Figure 5.23
Uniform probability distribution
Figure 5.24
Quantile function for normal distribution N(0,1)
Figure 5.25
Probability density of MFI results
Figure 5.26
Truncated PDF
Figure 5.27
Truncated CDF
Figure 5.28
Rectified PDF
Figure 5.29
Variation of predictability of coin toss
Chapter 06
Figure 6.1
Box and whisker diagram
Figure 6.2
Bins too wide
Figure 6.3
Bins too narrow
Figure 6.4
Using
Figure 6.5
Use of Surge’s formula to select number of bins
Figure 6.6
Poor choice of starting value for first bin
Figure 6.7
Use of Scott’s normal reference rule to select bin width
Figure 6.8
Optimised bin width
Figure 6.9
Conversion to probability density
Figure 6.10
Cumulative probability plot
Figure 6.11
Construction of kernel density plot
Figure 6.12
Effect of smoothing factor
Figure 6.13
Result of applying Silverman’s rule of thumb
Figure 6.14
Result of selecting Epanechnikov kernel
Figure 6.15
P–P plot demonstrating accuracy of fit
Figure 6.16
Distribution of C4 content of propane rundown
Figure 6.17
Comparison between kernel density and fitted normal distribution
Figure 6.18
Frequency–frequency plot demonstrating very poor fit
Figure 6.19
Use of radar plot to show days of off‐grade production
Figure 6.20
Use of radar plot to display MPC behaviour
Figure 6.21
Circular plot based on polar coordinates
Figure 6.22
Parallel coordinates
Figure 6.23
Use of pie chart to highlight quality control problem
Figure 6.24
Cumulative distribution of gasoil 95% with normal distribution fitted
Figure 6.25
P–P plot for gasoil 95%
Figure 6.26
Q–Q plot for gasoil 95%
Figure 6.27
Ranked versus paired points comparing inferential to on‐stream analyser
Figure 6.28
Procedure for adding missing quantiles
Figure 6.29
Q–Q plot including missing quantiles
Chapter 07
Figure 7.1
Impact of sample size on accuracy of skewness and kurtosis
Figure 7.2
Sample size necessary for estimating probability over a year
Figure 7.3
Application of Wald method for all future blends
Figure 7.4
Application of Agresti–Coull method for all future blends
Figure 7.5
Use of bootstrapping to determine confidence in estimating
μ
Chapter 08
Figure 8.1
Probability density of the number of heads from 100 tosses
Figure 8.2
Cumulative probability distribution of the number of heads
Figure 8.3
Confidence that coin is unbiased if it lands 60 (or 40) heads from 100 tosses
Figure 8.4
PDF showing probability of being within one standard deviation of the mean
Figure 8.5
CDF showing probability of being within one standard deviation of the mean
Figure 8.6
Confidence interval as a function of the number of standard deviations
Figure 8.7
Significance level versus confidence interval
Figure 8.8
Horwitz’s curve
Chapter 09
Figure 9.1
Error in estimating
σ
arising from error in estimating
μ
Figure 9.2
Empirical distribution function
Figure 9.3
Comparison between fitted and calculated distributions
Figure 9.4
P–P plots of fitted and calculated distributions
Figure 9.5
Impact of fixing
F(x
1
), F(x
n
) or F(x
n/
2
)
Figure 9.6
Including
F(x
1
)
among the parameters adjusted during fitting
Figure 9.7
P–P plot from fitting the PDF
Figure 9.8
Data presented as a histogram
Figure 9.9
Comparing derived probability distribution to histogram
Figure 9.10
P–P plot from fitting to the histogram
Figure 9.11
Anderson–Darling weighting factor
Figure 9.12
Kolmogorov–Smirnov penalty function
Figure 9.13
Impact of choice of penalty function
Chapter 10
Figure 10.1
Distribution of the ratio of two values selected from U(0,1)
Figure 10.2
Normal distribution fitted to reflux and distillate flows on LPG splitter
Figure 10.3
Variation of LPG splitter reflux ratio over time
Figure 10.4
Fitting normal and lognormal distributions to LPG splitter reflux ratio
Figure 10.5
Normal distribution fitted to reflux and distillate flows on debutaniser
Figure 10.6
Fitting the normal distribution to debutaniser reflux ratio
Figure 10.7
Distribution of the product of two values selected from U(0,1)
Figure 10.8
Normal distribution fitted to heat exchanger flow
Figure 10.9
Normal distribution fitted to heat exchanger temperature difference
Figure 10.10
Fitting normal and lognormal distributions to exchanger duty
Figure 10.11
Distribution of reciprocal of propane flow from LPG splitter
Figure 10.12
Normal distributions fitted to heat exchanger temperatures
Figure 10.13
Fitting normal and lognormal distributions to LMTD
Figure 10.14
Normal distribution fitted to LPG splitter pressure
Figure 10.15
Normal distribution fitted to LPG splitter tray temperature target
Figure 10.16
Close approximation to linearity between temperature and pressure
Figure 10.17
Impact of feed composition (
HK
f
) on distillate composition (
HK
d
)
Figure 10.18
Regressed relationship between distillate and feed compositions
Figure 10.19
Distribution of
HK
d
arising from normally distributed
HK
f
Figure 10.20
Normal distribution fitted to variation in viscosity blending number
Figure 10.21
Fitting normal and lognormal distributions to viscosities
Figure 10.22
Close approximation to linearity between VBN and viscosity
Figure 10.23
Normal distribution fitted to reactor temperature
Figure 10.24
Fitting normal and lognormal distributions to % converted
Figure 10.25
Fitting normal and lognormal distributions to % unconverted
Figure 10.26
Nonlinear relationship between conversion and reactor temperature
Figure 10.27
Distribution of root mean square of two values selected from N(0,1)
Figure 10.28
Fitting normal and lognormal distributions to root mean square flow
Chapter 11
Figure 11.1
Convergence to powers of Euler’s number
Figure 11.2
Euler–Mascheroni constant
Figure 11.3
Logit function
Figure 11.4
Logistic function
Figure 11.5
Gamma function
Figure 11.6
Log‐gamma function
Figure 11.7
Gamma function for negative values
Figure 11.8
Derivative of gamma function
Figure 11.9
Pochhammer ascending factorial
Figure 11.10
Pochhammer descending factorial
Figure 11.11
Modified Bessel function of the first kind
Figure 11.12
Convergence of Bessel function
Figure 11.13
Number of terms required to achieve 0.01% accuracy
Figure 11.14
Bessel function (of the first kind) restricted to integer orders
Figure 11.15
Modified Bessel function of the second kind
Figure 11.16
Bessel function (of the second kind) restricted to integer orders
Figure 11.17
Convergence of zeta function
Figure 11.18
Zeta function
Figure 11.19
Harmonic number
Figure 11.20
Accuracy of Stirling approximation
Chapter 12
Figure 12.1
Lognormal: Effect of
σ
on shape
Figure 12.2
Lognormal: Improved fit to the C
4
in propane data
Figure 12.3
Lognormal: P–P plot showing improved fit
Figure 12.4
Lognormal: PDF fitted to histogram of C
4
in propane data
Figure 12.5
Lognormal: Feasible combinations of
γ
and
κ
Figure 12.6
Burr‐XII: Fitted to the C
4
in propane data
Figure 12.7
Burr‐XII: Feasible combinations of
γ
and
κ
Figure 12.8
Burr‐XII: Fitted to the NHV disturbance data
Figure 12.9
Beta‐I: Effect of
δ
1
and δ
2
on shape
Figure 12.10
Beta‐I: Symmetric‐beta
(δ
1
= δ
2
)
Figure 12.11
Beta‐I: Effect of
δ
1
and
δ
2
on skewness
Figure 12.12
Beta‐I: Effect of
δ
1
and
δ
2
on kurtosis
Figure 12.13
Beta‐I: Conditions for zero kurtosis
Figure 12.14
Beta‐I: Impact of choice of range
Figure 12.15
Hosking: Impact of improved control of C
4
content of propane
Figure 12.16
Hosking: Fitted to the NHV disturbance data
Figure 12.17
Hosking: Fitted to absolute changes in NHV
Figure 12.18
Hosking: Exponential distributions as special case
Figure 12.19
Hosking: Generalised Pareto distribution as special case
Figure 12.20
Hosking: Generalised extreme value distribution as special case
Figure 12.21
Hosking: Other special cases
Figure 12.22
Gumbel: Effect of
α
and
β
on shape
Figure 12.23
Hosking: Unnamed distribution as special case
Figure 12.24
Hosking: Summary of distributions represented
Figure 12.25
Student: Probability density compared to normal distribution
Figure 12.26
Student: Effect of
f
on cumulative distribution
Figure 12.27
Student: Detail of effect of
f
on cumulative distribution
Figure 12.28
Fisher: Effect of
f
1
on shape (
f
2
= 1)
Figure 12.29
Fisher: Effect of
f
1
on shape (
f
2
= 3)
Figure 12.30
Fisher: Effect of
f
1
on shape (
f
2
= 100
)
Figure 12.31
Fisher: Feasible combinations of
γ
and
κ
Figure 12.32
Exponential: Application to WECO rules and stock level example
Figure 12.33
Exponential: Fitted to interval between high reflux flow events
Figure 12.34
Weibull‐I: Effect of
δ
on shape
Figure 12.35
Weibull‐II: Effect of
δ
and
β
on shape
Figure 12.36
Weibull‐II: Alternative method of fitting to changes in C
4
content of propane
Figure 12.37
Weibull: Feasible combinations of
γ
and
κ
Figure 12.38
Weibull‐II: Method of fitting to stock level data
Figure 12.39
Weibull‐II: Result of fitting to stock level data
Figure 12.40
Chi‐squared: Probability density for
f =
1 and
f =
2
Figure 12.41
Chi‐squared: Probability density for
f ≥
3
Figure 12.42
Chi‐squared: Cumulative probability
Figure 12.43
Chi‐squared: Assessing reliability of predicted values
Figure 12.44
Gamma: Effect of
k
and
β
on shape
Figure 12.45
Gamma: Feasible combinations of
γ
and
κ
Figure 12.46
Gamma: Cumulative distribution
Figure 12.47
Gamma: Probability distribution of time to produce a batch
Figure 12.48
Gamma: Probability distribution of required inventory
Figure 12.49
Binomial: Fitting a normal distribution to the number of sixes from 12 throws
Figure 12.50
Binomial: Minimum number of trials for normal distribution to be applicable
Figure 12.51
Binomial: Demonstration that normal distribution can be used for
n =
36
Figure 12.52
Binomial: Likely failure rate for an inferential
Figure 12.53
Binomial: Reducing the average number of off‐grade results for diesel
Figure 12.54
Binomial: Estimating the reduction in the likely number of off‐grade results
Figure 12.55
Poisson: Effect of
λ
on probability distribution
Figure 12.56
Poisson: Effect of
λ
on cumulative probability distribution
Chapter 13
Figure 13.1
Frequency distribution of extreme reflux flow (24‐hour maxima)
Figure 13.2
Fit of GEV distribution to 24‐hour maxima
Figure 13.3
Frequency distribution of reflux flow (48‐hour maxima)
Figure 13.4
Fit of GEV and extreme value distributions to 48‐hour maxima
Figure 13.5
Frequency distribution of reflux exceedances (>66.5)
Figure 13.6
Fit of generalised Pareto distribution to exceedances (>66.5)
Figure 13.7
Frequency distribution of reflux exceedances (>75.8)
Figure 13.8
Fit of generalised Pareto distribution to exceedances (>75.8)
Figure 13.9
Frequency distribution of reflux flow (72‐hour minima)
Figure 13.10
Fit of GEV distribution to 72‐hour minima
Figure 13.11
Frequency distribution of reflux exceedances (<34.2)
Figure 13.12
Fit of generalised Pareto distribution to exceedances (<34.2)
Chapter 14
Figure 14.1
Hazard function derived from EL distribution
Figure 14.2
Cumulative hazard function derived from EL distribution
Figure 14.3
Distribution of intervals between high reflux flow events
Figure 14.4
Fit of EL distribution to intervals between high reflux flow events
Figure 14.5
Reduction in frequency of events assuming EL distribution
Figure 14.6
Hazard function derived from gamma distribution
Figure 14.7
Hazard function derived from Weibull distribution
Figure 14.8
Reduction in frequency of events assuming Weibull distribution
Figure 14.9
Fit of Weibull distribution to intervals between high reflux flow events
Figure 14.10
Bathtub curve for advanced control application
Figure 14.11
Hjorth hazard function: Effect of
δ
1
and
δ
2
Chapter 15
Figure 15.1
Error between inferential for C
3
in butane and the on‐stream analyser
Figure 15.2
Trend of cumulative sum of error
Figure 15.3
Fit of Weibull‐II distribution to interval between errors exceeding 0.5 vol%
Figure 15.4
Demonstrating that the process has memory
Figure 15.5
Comparison between speeds at which bias error is removed
Figure 15.6
Trend of cumulative sum of deviation of stock level from the mean
Chapter 16
Figure 16.1
Minimisation of the total sum of the squares in
y
direction
Figure 16.2
Linear regression analysis
Figure 16.3
Compensation of one independent variable for variation in others
Figure 16.4
Minimisation of the total sum of the squares in
x
direction
Figure 16.5
Minimisation of the total sum of the squares of the perpendicular distance
Figure 16.6
Minimisation of the total sum of the rectangles in
x
and
y
direction
Figure 16.7
Impact of choice of penalty function
Figure 16.8
Detection that a nonlinear correlation should be used
Figure 16.9
Single input inferentials
Figure 16.10
Two‐input inferential
Figure 16.11
Correlation between inputs
Figure 16.12
Probability that two‐input inferential is better than single input version
Figure 16.13
Structure of artificial neural network
Figure 16.14
Sigmoid curves
Figure 16.15
Artificial neural network outperforming linear regression
Figure 16.16
Validation of inferential based on artificial neural network
Figure 16.17
Advanced control vendor stock price
Figure 16.18
Predicting stock price
Figure 16.19
Inferential performance index
Chapter 17
Figure 17.1
Noisy measurement
Figure 17.2
Oscillation detected by autocorrelation
Figure 17.3
Comparison between on‐stream analyser and inferential
Figure 17.4
Effect of time delay on correlation
Figure 17.5
Autocorrelation of stock levels
Figure 17.6
Accuracy of predicted stock level
Chapter 18
Figure 18.1
Reconciliation of two measurements
Figure 18.2
Reconciliation of three measurements
Figure 18.3
Minimisation of data reconciliation penalty function
Chapter 19
Figure 19.1
Arctangent2 function
Figure 19.2
Apparently noisy measurement
Figure 19.3
Power (or frequency) spectrum
Figure 19.4
Period spectrum
Figure 19.5
Phase spectrum
Figure 19.6
Superimposition of dominant wave form on original measurement
Figure 19.7
Frequency spectrum derived with two additional data points
Figure 19.8
Addition of second noisy measurement
Figure 19.9
No apparent correlation between measurements
Figure 19.10
Correlation between frequency spectra
Chapter 20
Figure 20.1
Skew‐normal: Effect of
δ
on shape
Figure 20.2
Skew‐normal: Effect of
δ
on skewness and kurtosis
Figure 20.3
Skew‐normal: Impact
δ
has on fitting to C
4
in propane data
Figure 20.4
Skew‐normal: Feasible combinations of
γ
and
κ
Figure 20.5
Power lognormal: Effect of
p
on shape
Figure 20.6
Logit‐normal: Effect of
β
on shape
Figure 20.7
Logit‐normal: Effect of
α
on shape
Figure 20.8
Folded normal: Effect of
α
on shape
Figure 20.9
Levy: Effect of
β
on shape
Figure 20.10
Levy: Poor fit to absolute changes in NHV
Figure 20.11
Inverse Gaussian: Effect of
σ
on shape
Figure 20.12
Inverse Gaussian: Effect of
μ
and
σ
on skewness
Figure 20.13
Inverse Gaussian: Effect of
μ
and
σ
on kurtosis
Figure 20.14
Inverse Gaussian: Feasible combinations of
γ
and
κ
Figure 20.15
Inverse Gaussian: Fitted to the C
4
in propane data
Figure 20.16
Inverse Gaussian: P–P plot showing improved fit to C
4
data
Figure 20.17
Inverse Gaussian: Fit to histogram of C
4
in propane data
Figure 20.18
Generalised inverse Gaussian: Effect of
β
and
δ
on shape
Figure 20.19
Normal inverse Gaussian: Effect of
δ
on shape
Figure 20.20
Normal inverse Gaussian: Effect of
λ
on shape
Figure 20.21
Normal inverse Gaussian: Effect of
β
on shape
Figure 20.22
Reciprocal inverse Gaussian: Effect of
α
and
λ
on shape
Figure 20.23
Reciprocal inverse Gaussian: Fitted to the C
4
in propane data
Figure 20.24
Q‐Gaussian: Effect of
q
on shape
Figure 20.25
Q‐Gaussian: Effect of
q
on kurtosis, keeping
σ
fixed
Figure 20.26
Q‐Gaussian: Effect of
q
on kurtosis
Figure 20.27
Q‐Gaussian: Fitted to the NHV disturbance data
Figure 20.28
Q‐Gaussian: P–P plot showing improved fit to NHV data
Figure 20.29
Generalised error: Effect of
δ
on shape
Figure 20.30
Generalised error: Effect of
δ
on kurtosis
Figure 20.31
Generalised error: Fitted to the NHV disturbance data
Figure 20.32
Generalised error: Impact
δ
has on fitting to NHV data
Figure 20.33
Generalised error: Impact
δ
has on estimating
σ
Figure 20.34
Generalised normal (2): Effect of
β
on shape
Figure 20.35
Generalised normal (2): Effect of
δ
on shape
Figure 20.36
Generalised normal (2): Effect of
δ
on
γ
and
κ
Figure 20.37
Generalised normal (2): Feasible combinations of
γ
and
κ
Figure 20.38
Generalised normal (3): Effect of
δ
1
and
δ
2
on shape
Figure 20.39
Generalised normal (3): Feasible combinations of
γ
and
κ
Figure 20.40
Exponentially modified Gaussian: Effect of
λ
on shape
Figure 20.41
Exponentially modified Gaussian: Feasible combinations of
γ
and
κ
Figure 20.42
Moyal: Effect of
β
on shape
Chapter 21
Figure 21.1
Burr‐III: Effect of
δ
1
and
δ
2
on shape
Figure 21.2
Burr‐IV: Effect of
δ
1
and
δ
2
on shape
Figure 21.3
Burr‐V: Effect of
δ
1
and
δ
2
on shape
Figure 21.4
Burr‐VI: Effect of
δ
1
and
δ
2
on shape
Figure 21.5
Burr‐VII: Effect of
δ
on shape
Figure 21.6
Burr‐VIII: Effect of
δ
on shape
Figure 21.7
Burr‐IX: Effect of
δ
1
and
δ
2
on shape
Figure 21.8
Burr‐X: Effect of
δ
on shape
Figure 21.9
Burr‐XI: Effect of
δ
on shape
Figure 21.10
Dagum‐I: Effect of
δ
1
on shape
Figure 21.11
Dagum‐I: Effect of
δ
2
on shape
Figure 21.12
Dagum‐I: Feasible combinations of
γ
and
κ
Chapter 22
Figure 22.1
Logistic: Effect of
δ
on shape
Figure 22.2
Logistic: Approximation to normal distribution
Figure 22.3
Half‐logistic: Effect of
λ
on shape
Figure 22.4
Skew‐logistic (1): Effect of
δ
on shape
Figure 22.5
Skew‐logistic (2): Effect of
δ
on shape
Figure 22.6
Log‐logistic: Effect of
α
,
β
and
δ
on shape
Figure 22.7
Log‐logistic: Fitted to the C
4
in propane data
Figure 22.8
Log‐logistic: Feasible combinations of
γ
and
κ
Figure 22.9
Paralogistic: Effect of
δ
on shape
Figure 22.10
Paralogistic: Feasible combinations of
γ
and
κ
Figure 22.11
Paralogistic: Fitted to the C
4
in propane data
Figure 22.12
Generalised logistic‐I: Effect of
δ
on shape
Figure 22.13
Generalised logistic‐II: Effect of
δ
on shape
Figure 22.14
Generalised logistic‐III: Effect of
δ
on shape
Figure 22.15
Generalised logistic‐IV: Effect of
δ
1
on shape
Figure 22.16
Generalised logistic‐IV: Effect of
δ
2
on shape
Figure 22.17
Generalised log‐logistic: Effect of
δ
1
and
δ
2
on shape
Chapter 23
Figure 23.1
Pareto‐I: Effect of
β
and
δ
on shape
Figure 23.2
Observed distribution of absolute change in NHV
Figure 23.3
Pareto‐II: Effect of
β
and
δ
on shape
Figure 23.4
Inverse Pareto: Effect of
δ
on shape
Figure 23.5
Pareto‐III: Effect of
δ
on shape
Figure 23.6
Generalised Pareto: Effect of
δ
on shape
Figure 23.7
Generalised Pareto: Feasible combinations of
γ
and
κ
Figure 23.8
Lorenz curve
Figure 23.9
Pareto analysis
Chapter 24
Figure 24.1
Stoppa‐II: Effect of
δ
2
on shape
Figure 24.2
Stoppa‐II: Fitted to the NHV disturbance data
Figure 24.3
Stoppa‐IV: Effect of
δ
on shape
Chapter 25
Figure 25.1
Arcsine distributions
Figure 25.2
Wigner semicircle
Figure 25.3
Beta‐II: Comparison to the beta‐I distribution fitted to the C
4
data
Figure 25.4
Beta‐II: Effect of
δ
1
and
δ
2
on skewness
Figure 25.5
Beta‐II: Effect of
δ
1
and
δ
2
on kurtosis
Figure 25.6
Beta‐II: Feasible combinations of
γ
and
κ
Figure 25.7
Generalised beta prime: Effect of
δ
1
, δ
2
and
δ
3
on shape
Figure 25.8
PERT: Effect of
λ
on shape
Figure 25.9
Beta rectangular: Effect of
δ
on shape
Figure 25.10
Kumaraswamy: Effect of
δ
1
on shape
Figure 25.11
Kumaraswamy: Effect of
δ
2
on shape
Figure 25.12
Kumaraswamy: Feasible combinations of
γ
and
κ
Figure 25.13
Minimax odds: Effect of
δ
1
and
δ
2
on shape
Chapter 26
Figure 26.1
Johnson S
N
: Effect of
α
and
β
on shape
Figure 26.2
Johnson S
U
: Comparison with Johnson S
N
distribution
Figure 26.3
Johnson S
U
: Effect of
α
and
β
on shape
Figure 26.4
Johnson S
L
: Effect of
α
and
β
on shape
Figure 26.5
Johnson S
B
: Effect of
α
and
β
on shape
Chapter 27
Figure 27.1
Pearson: Range of
γ
and
κ
covered
Figure 27.2
Pearson‐III: Effect of
δ
on shape
Figure 27.3
Pearson‐III: Feasible combinations of
γ
and
κ
Figure 27.4
Pearson‐IV: Effect of
δ
2
on shape
Figure 27.5
Pearson‐IV: Feasible combinations of
γ
and
κ
Figure 27.6
Cauchy: Effect of
α
and
β
on shape
Figure 27.7
Cauchy: Fitted to NHV disturbances
Figure 27.8
Log‐Cauchy: Effect of
α
on shape
Figure 27.9
Log‐Cauchy: Effect of
β
on shape
Figure 27.10
Log‐Cauchy: P–P plot showing fit to absolute changes in NHV
Figure 27.11
Log‐Cauchy: Plot of PDF fitted to absolute changes in NHV
Figure 27.12
Pearson‐V: Effect of
δ
on shape
Figure 27.13
Pearson‐VI: Effect of
δ
1
and
δ
2
on shape
Figure 27.14
Pearson‐VI: Relationship between
RSS
and
σ
Figure 27.15
Pearson‐VI: Feasible combinations of
γ
and
κ
Figure 27.16
Log‐F: Effect of
f
1
and
f
2
on shape
Figure 27.17
Pearson‐VII: Effect of
δ
on shape
Figure 27.18
Log‐Student: Effect of
f
on shape
Figure 27.19
Noncentral Student: Effect of
δ
on shape
Figure 27.20
Noncentral Student: Fitted to the C
4
in propane data
Chapter 28
Figure 28.1
Hyperexponential: Cumulative probability of interval between events
Figure 28.2
Hypoexponential: Effect of
λ
1
and
λ
2
on shape
Figure 28.3
Exponential: Comparison between versions
Figure 28.4
Maxwell–Jüttner: Effect of
λ
on shape
Figure 28.5
Stretched exponential: Effect of
δ
on shape
Figure 28.6
Exponential logarithmic: Effect of
λ
and
δ
on shape
Figure 28.7
Logistic exponential: Effect of
λ
and
δ
on shape
Figure 28.8
Q‐exponential: Effect of
q
and
λ
on shape
Figure 28.9
Q‐exponential: Improved fit to absolute changes in NHV
Figure 28.10
Benktander‐I: Effect of
λ
and
δ
on shape
Figure 28.11
Benktander‐II: Effect of
λ
and
δ
on shape
Chapter 29
Figure 29.1
Nukiyama–Tanasawa: Effect of
δ
1
on shape
Figure 29.2
Q‐Weibull: Effect of
q
on shape with
δ
= 1
Figure 29.3
Q‐Weibull: Effect of
q
on shape with
δ
= 2
Figure 29.4
Q‐Weibull: Improved fit to stock level data
Chapter 30
Figure 30.1
Chi: Effect of
f
on shape
Figure 30.2
Rayleigh: Effect of
β
on shape
Figure 30.3
Inverse Rayleigh: Effect of
β
on shape
Figure 30.4
Maxwell: Effect of
β
on shape
Figure 30.5
Chi: Feasible combinations of
γ
and
κ
Figure 30.6
Chi: Fitted to changes in C
4
content of propane
Figure 30.7
Inverse chi: Effect of
f
on shape
Figure 30.8
Inverse chi‐squared: Effect of
f
on shape
Figure 30.9
Inverse chi‐squared: Feasible combinations of
γ
and
κ
Figure 30.10
Noncentral chi‐squared: Effect of
δ
and
β
on shape
Chapter 31
Figure 31.1
Log‐gamma (1): Effect of
δ
1
and
δ
2
on shape
Figure 31.2
Log‐gamma (2): Effect of
δ
1
and
δ
2
on shape
Figure 31.3
Log‐gamma (3): Effect of
δ
1
and
δ
2
on shape
Figure 31.4
Log‐gamma (4): Effect of
δ
1
and
δ
2
on shape
Figure 31.5
Log‐gamma (5): Effect of
δ
on shape
Figure 31.6
Generalised gamma: Problem fitting to C
4
in propane data
Figure 31.7
Q‐gamma: Effect of
q
on shape
Chapter 32
Figure 32.1
Anglit: Effect of
μ
and
β
on shape
Figure 32.2
Bates: Effect of
n
on shape
Figure 32.3
Irwin–Hall: Effect of
n
on shape
Figure 32.4
Hyperbolic secant: Effect of
μ
and
σ
on shape
Figure 32.5
Arctangent: Effect of
δ
and
β
on shape
Figure 32.6
Arctangent: Poor fit to NHV disturbance data
Figure 32.7
Kappa: Effect of
δ
on shape
Figure 32.8
Laplace: Effect of
μ
and
σ
on shape
Figure 32.9
Cosine: Effect of
μ
and
β
on shape
Figure 32.10
Raised cosine: Effect of
μ
and
β
on shape
Figure 32.11
Cardioid: Circular plot showing effect of
β
on shape
Figure 32.12
Cardioid: Conventional plot showing effect of
β
on shape
Figure 32.13
Slash: Effect of
μ
and
σ
on shape
Figure 32.14
Tukey lambda: Effect of
λ
on shape
Figure 32.15
Tukey lambda: Effect of
λ
on kurtosis
Figure 32.16
Von Mises: Effect of
β
on shape
Figure 32.17
Von Mises: Estimating
σ
from
β
Chapter 33
Figure 33.1
Benini: Effect of
α
and
β
on shape
Figure 33.2
Birnbaum–Saunders: Effect of
δ
on shape
Figure 33.3
Birnbaum–Saunders: Feasible combinations of
γ
and
κ
Figure 33.4
Bradford: Effect of
λ
on shape
Figure 33.5
Champernowne (1): Effect of
δ
1
and
δ
2
on shape
Figure 33.6
Champernowne (2): Effect of
δ
1
and
δ
2
on shape
Figure 33.7
Champernowne (2): Feasible combinations of
γ
and
κ
Figure 33.8
Davis: Effect of
δ
on shape
Figure 33.9
Fréchet: Effect of
δ
and
β
on shape
Figure 33.10
Fréchet: Feasible combinations of
γ
and
κ
Figure 33.11
Fréchet: Fitted to C
4
in propane data
Figure 33.12
Gompertz: Effect of
α
and
β
on shape
Figure 33.13
Shifted Gompertz: Effect of
α
on shape
Figure 33.14
Gompertz–Makeham: Effect of
α
,
β
and
λ
on shape
Figure 33.15
Gamma‐Gompertz: Effect of
α
,
β
and
δ
on shape
Figure 33.16
Gompertz: Comparison of fits to C
4
in propane data
Figure 33.17
Hyperbolic: Effect of
δ
on shape
Figure 33.18
Hyperbolic: Effect of
λ
on shape
Figure 33.19
Asymmetric Laplace: Effect of
δ
on shape
Figure 33.20
Asymmetric Laplace: Feasible combinations of
γ
and
κ
Figure 33.21
Log‐Laplace (1): Effect of
α
and
β
on shape
Figure 33.22
Log‐Laplace (2): Effect of
δ
on shape
Figure 33.23
indley: Effect of
λ
on shape
Figure 33.24
Lindley: Feasible combinations of
γ
and
κ
Figure 33.25
Lindley‐geometric: Effect of
δ
on shape
Figure 33.26
Generalised Lindley: Effect of
δ
1
and
δ
2
on shape
Figure 33.27
Lindley: Comparison of fits to C
4
in propane data
Figure 33.28
Mielke: Effect of
δ
1
and
δ
2
on shape
Figure 33.29
Muth: Effect of
δ
on shape
Figure 33.30
Nakagami: Effect of
δ
on shape
Figure 33.31
Nakagami: Data ignored when fitted to C
4
in propane data
Figure 33.32
Power: Effect of
δ
on shape
Figure 33.33
Power: Feasible combinations of
γ
and
κ
Figure 33.34
Two‐sided power: Effect of
δ
on shape
Figure 33.35
Exponential power: Effect of
λ
and
δ
on shape
Figure 33.36
Rician: Effect of
α
on shape
Figure 33.37
Topp–Leone: Effect of
δ
on shape
Figure 33.38
Generalised Tukey: Effect of
λ
3
and
λ
4
on shape
Figure 33.39
Generalised Tukey: One of the best fits to NHV disturbance data
Figure 33.40
Generalised Tukey: One of the best fits to the C
4
in propane data
Figure 33.41
Wakeby: Effect of
δ
1
on shape
Figure 33.42
Wakeby: Effect of
δ
2
on shape
Figure 33.43
Wakeby: Effect of
δ
3
on shape
Figure 33.44
Wakeby: Effect of
δ
4
on shape
Figure 33.45
Wakeby: Improving the fit to the C
4
in propane data
Chapter 34
Figure 34.1
Amoroso: Effect of
δ
1
and
δ
2
on shape
Figure 34.2
Amoroso: Fitted to the C
4
in propane data
Figure 34.3
Amoroso: Feasible combinations of
γ
and
κ
Chapter 35
Figure 35.1
Negative binomial: Fit to batch blending performance
Figure 35.2
Use of same percentage rule to quantify control improvement
Figure 35.3
Cumulative frequency showing intersection at same percentage
Figure 35.4
Geometric: Impact of improved control on distribution of days required per batch
Figure 35.5
Geometric: Reduction in probability of large number of trim blends
Figure 35.6
Beta‐geometric: Effect of
α
and
β
on shape
Figure 35.7
Beta‐geometric: Fit to interval between high reflux events
Figure 35.8
Beta‐geometric: 95% confidence that high reflux event occurs within 5 days
Figure 35.9
Beta‐binomial: Effect of
α
and
β
on shape
Figure 35.10
Beta‐binomial: Fitted to frequency of high reflux events
Figure 35.11
Beta‐binomial: Improvement on accuracy of fit of binomial distribution
Figure 35.12
Beta‐negative binomial: Effect of
α
and
β
on shape
Figure 35.13
Beta‐Pascal: Effect of
α
and
β
on shape
Figure 35.14
Gamma‐Poisson: Effect of
α
and
β
on shape
Figure 35.15
Gamma‐Poisson: Improved fit to frequency of reflux events
Figure 35.16
Gamma‐Poisson: Accurate representation of number of events per day
Figure 35.17
Conway–Maxwell–Poisson: Effect of
δ
on shape
Figure 35.18
Conway–Maxwell–Poisson: Alternative method of fitting to data
Figure 35.19
Skellam: Approximation to normal distribution
Figure 35.20
Skellam: Probability of reducing the number of low‐stock incidents
Chapter 36
Figure 36.1
Benford: Expected and actual distribution of leading digit in accounts
Figure 36.2
Benford: P–P plot showing exception from expected distribution
Figure 36.3
Benford: Expected distribution of two leading digits
Figure 36.4
Benford: Expected distribution of second digit
Figure 36.5
Benford: Expected and actual distribution of atomic weights
Figure 36.6
Borel–Tanner: Effect of
λ
on shape
Figure 36.7
Borel–Tanner: Effect of
n
on shape
Figure 36.8
Borel–Tanner: Impact of increased production on likelihood of completion
Figure 36.9
Borel–Tanner: Impact of restricted increase in laboratory capacity
Figure 36.10
Consul: Effect of
α
and
β
on shape
Figure 36.11
Delaporte: Effect of
λ
on shape
Figure 36.12
Delaporte: Effect of
α
and
β
on shape
Figure 36.13
Delaporte: Fit to frequency of high reflux events
Figure 36.14
Flory–Schulz: Effect of
p
on shape
Figure 36.15
Hypergeometric: Effect of
K
on shape
Figure 36.16
Negative hypergeometric: Effect of
n
1
on shape
Figure 36.17
Logarithmic: Effect of
p
on shape
Figure 36.18
Logarithmic: Fit to number of blends require per batch
Figure 36.19
Discrete Weibull: Effect of
β
on shape
Figure 36.20
Zipf: Actual distribution against that expected from ranking
Figure 36.21
Zipf: P–P plot showing close match for almost all words
Figure 36.22
Zipf: Demonstration of king effect
Guide
Cover
Table of Contents
Begin Reading
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Statistics for Process Control Engineers
A Practical Approach
Myke King
Whitehouse Consulting, Isle of Wight, UK
This edition first published 2017© 2017 John Wiley & Sons Ltd
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Library of Congress Cataloging‐in‐Publication Data
Names: King, Myke, 1951–Title: Statistics for process control engineers : a practical approach / Myke King.Description: First edition. | Hoboken, NJ : Wiley, [2017] | Includes bibliographical references and index.Identifiers: LCCN 2017013231 (print) | LCCN 2017015732 (ebook) | ISBN 9781119383482 (pdf) ISBN 9781119383529 (epub) | ISBN 9781119383505 (cloth)Subjects: LCSH: Process control--Mathematical models. | Engineering–Statistical methods. | Engineering mathematics.Classification: LCC TS156.8 (ebook) | LCC TS156.8 .K487 2018 (print) | DDC 620.001/51--dc23LC record available at https://lccn.loc.gov/2017013231
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Preface
There are those that have a very cynical view of statistics. One only has to search the Internet to find quotations such as those from the author Mark Twain:
There are three kinds of lies: lies, damned lies, and statistics.Facts are stubborn, but statistics are more pliable.
From the American humourist Evan Esar:
Statistics is the science of producing unreliable facts from reliable figures.
From the UK’s shortest‐serving prime minister George Canning:
I can prove anything by statistics except the truth.
And my personal favourite, attributed to many – all quoting different percentages!
76.3% of statistics are made up.
However, in the hands of a skilled process control engineer, statistics are an invaluable tool. Despite advanced control technology being well established in the process industry, the majority of site managers still do not fully appreciate its potential to improve process profitability. An important part of the engineer’s job is to present strong evidence that such improvements are achievable or have been achieved. Perhaps one of the most insightful quotations is that from the physicist Ernest Rutherford.
If your experiment needs statistics, you ought to have done a better experiment.
Paraphrasing for the process control engineer:
If you need statistics to demonstrate that you have improved control of the process, you ought to have installed a better control scheme.
Statistics is certainly not an exact science. Like all the mathematical techniques that are applied to process control, or indeed to any branch of engineering, they need to be used alongside good engineering judgement. The process control engineer has a responsibility to ensure that statistical methods are properly applied. Misapplied they can make a sceptical manager even more sceptical about the economic value of improved control. Properly used they can turn a sceptic into a champion. The engineer needs to be well versed in their application. This book should help ensure so.
After writing the first edition of Process Control: A Practical Approach, it soon became apparent that not enough attention was given to the subject. Statistics are applied extensively at every stage of a process control project from estimation of potential benefits, throughout control design and finally to performance monitoring. In the second edition this was partially addressed by the inclusion of an additional chapter. However, in writing this, it quickly became apparent that the subject is huge. In much the same way that the quantity of published process control theory far outstrips more practical texts, the same applies to the subject of statistics – but to a much greater extent. For example, the publisher of this book currently offers over 2,000 titles on the subject but fewer than a dozen covering process control. Like process control theory, most published statistical theory has little application to the process industry, but within it are hidden a few very valuable techniques.
Of course, there are already many statistical methods routinely applied by control engineers – often as part of a software product. While many use these methods quite properly, there are numerous examples where the resulting conclusion later proves to be incorrect. This typically arises because the engineer is not fully aware of the underlying (incorrect) assumptions behind the method. There are also too many occasions where the methods are grossly misapplied or where licence fees are unnecessarily incurred for software that could easily be replicated by the control engineer using a spreadsheet package.
This book therefore has two objectives. The first is to ensure that the control engineer properly understands the techniques with which he or she might already be familiar. With the rapidly widening range of statistical software products (and the enthusiastic marketing of their developers), the risk of misapplication is growing proportionately. The user will reach the wrong conclusion about, for example, the economic value of a proposed control improvement or whether it is performing well after commissioning. The second objective is to extract, from the vast array of less well‐known statistical techniques, those that a control engineer should find of practical value. They offer the opportunity to greatly improve the benefits captured by improved control.
A key intent in writing this book was to avoid unnecessarily taking the reader into theoretical detail. However the reader is encouraged to brave the mathematics involved. A deeper understanding of the available techniques should at least be of interest and potentially of great value in better understanding services and products that might be offered to the control engineer. While perhaps daunting to start with, the reader will get the full value from the book by reading it from cover to cover. A first glance at some of the mathematics might appear complex. There are symbols with which the reader may not be familiar. The reader should not be discouraged. The mathematics involved should be within the capabilities of a high school student. Chapters 4 to 6 take the reader through a step‐by‐step approach introducing each term and explaining its use in context that should be familiar to even the least experienced engineer. Chapter 11 specifically introduces the commonly used mathematical functions and their symbology. Once the reader’s initial apprehension is overcome, all are shown to be quite simple. And, in any case, almost all exist as functions in the commonly used spreadsheet software products.
It is the nature of almost any engineering subject that the real gems of useful information get buried among the background detail. Listed here are the main items worthy of special attention by the engineer because of the impact they can have on the effectiveness of control design and performance.
Control engineers use the terms ‘accuracy’ and ‘precision’ synonymously when describing the confidence they might have in a process measurement or inferential property. As explained in
Chapter 4
, not understanding the difference between these terms is probably the most common cause of poorly performing quality control schemes.
