Handbook of Industrial Engineering Equations, Formulas, and Calculations | Adedeji Badiru and Olufemi A. Omitaomu

By

Handbook of Industrial Engineering Equations, Formulas, and Calculations
by Adedeji Badiru and Olufemi A. Omitaomu

Handbook of Industrial Engineering Equations, Formulas, and Calculations

Contents

Preface . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . xxix
Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . xxxi
1 Computational Foundations of Industrial Engineering
Efficacy of Mathematical Modeling …………………………………………………………………….1-1
Industrial Engineering and Computations …………………………………………………………..1-1
Definition and Applications ……………………………………………………………………………….1-5
Orientation to STEM………………………………………………………………………………………….1-6
IE Catchphrases …………………………………………………………………………………………………1-6
Span and Utility of IE …………………………………………………………………………………………1-6
Heritage from Industrial Revolution……………………………………………………………………1-7
Historical Accounts ……………………………………………………………………………………………1-8
Chronology of Applications………………………………………………………………………………1-10
Importance of IE Calculations ……………………………………………………………………1-14
Importance of Calculations Guide …………………………………………………………………….1-16
Basic Queuing Equations ………………………………………………………………………………….1-17
Queuing Birth–Death Processes………………………………………………………………………..1-21
Laws of Motion of Queuing Birth and Death ……………………………………………………..1-21
Queuing Birth–Death Law 1 ………………………………………………………………………1-21
Queuing Birth–Death Law 2 ………………………………………………………………………1-21
Queuing Birth–Death Law 3 ………………………………………………………………………1-21
Data Types for Computational Analysis …………………………………………………………….1-22
Nominal Scale …………………………………………………………………………………………..1-22
Ordinal Scale …………………………………………………………………………………………….1-22
Interval Scale …………………………………………………………………………………………….1-22
Ration Scale ………………………………………………………………………………………………1-23
Cardinal Scale……………………………………………………………………………………………1-23
References ……………………………………………………………………………………………………….1-23
2 Basic Mathematical Calculations
Quadratic Equation ……………………………………………………………………………………………2-1
Overall Mean……………………………………………………………………………………………………..2-2
Chebyshev’s Theorem ………………………………………………………………………………………..2-2
Permutations……………………………………………………………………………………………………..2-2
Combinations ……………………………………………………………………………………………………2-2
Failure ………………………………………………………………………………………………………..2-3
Probability Distribution ……………………………………………………………………………………..2-3
Probability…………………………………………………………………………………………………………2-3
Distribution Function ………………………………………………………………………………………..2-3
Expected Value ………………………………………………………………………………………………….2-4
Variance ……………………………………………………………………………………………………………2-5
Binomial Distribution ………………………………………………………………………………………..2-5
Poisson Distribution…………………………………………………………………………………………..2-5
Mean of a Binomial Distribution…………………………………………………………………………2-6
Normal Distribution…………………………………………………………………………………………..2-6
Cumulative Distribution Function………………………………………………………………………2-6
Population Mean ……………………………………………………………………………………………….2-6
Standard Error of the Mean………………………………………………………………………………..2-6
t-Distribution…………………………………………………………………………………………………….2-7
Chi-Squared Distribution …………………………………………………………………………………..2-7
Definition of Set and Notation ……………………………………………………………………………2-7
Set Terms and Symbols ………………………………………………………………………………………2-8
Venn Diagrams………………………………………………………………………………………………….2-8
Operations on Sets……………………………………………………………………………………………..2-9
De Morgan’s Laws ……………………………………………………………………………………………..2-9
Counting the Elements in a Set………………………………………………………………………….2-10
Permutations……………………………………………………………………………………………………2-10
Combinations ………………………………………………………………………………………………….2-11
Probability Terminology…………………………………………………………………………………..2-11
Basic Probability Principles ………………………………………………………………………………2-11
Random Variable……………………………………………………………………………………………..2-12
Mean Value ˆx or Expected Value μ …………………………………………………………………..2-12
Series Expansions …………………………………………………………………………………………….2-12
Mathematical Signs and Symbols ………………………………………………………………………2-15
Greek Alphabets ………………………………………………………………………………………………2-16
Algebra ……………………………………………………………………………………………………………2-17
Laws of Algebraic Operations …………………………………………………………………….2-17
Special Products and Factors ……………………………………………………………………..2-17
Powers and Roots………………………………………………………………………………………2-19
Proportion ………………………………………………………………………………………………..2-19
Sum of Arithmetic Progression to n Terms …………………………………………………2-20
Sum of Geometric Progression to n Terms………………………………………………….2-20
Arithmetic Mean of n Quantities, A……………………………………………………………2-20
Geometric Mean of n Quantities, G ……………………………………………………………2-20
Harmonic Mean of n Quantities, H …………………………………………………………………..2-20
Generalized Mean……………………………………………………………………………………..2-20
Solution of Quadratic Equations ………………………………………………………………..2-21
Solution of Cubic Equations ………………………………………………………………………2-21
Trigonometric Solution of the Cubic Equation ……………………………………………2-22
Solution of Quadratic Equations ……………………………………………………………………….2-23
Partial Fractions……………………………………………………………………………………………….2-23
Nonrepeated Linear Factors……………………………………………………………………….2-23
Repeated Linear Factors …………………………………………………………………………….2-24
General terms…………………………………………………………………………………………………..2-24
Repeated Linear Factors …………………………………………………………………………….2-25
Factors of Higher Degree ………………………………………………………………………………….2-25
Geometry…………………………………………………………………………………………………………2-25
Triangles …………………………………………………………………………………………………..2-25
Right Triangle …………………………………………………………………………………………..2-26
Equilateral Triangle …………………………………………………………………………………..2-26
General Triangle ……………………………………………………………………………………….2-26
Menelaus’ Theorem………………………………………………………………………………………….2-27
Ceva’s Theorem ……………………………………………………………………………………………….2-27
Quadrilaterals ………………………………………………………………………………………………….2-27
Rectangle ………………………………………………………………………………………………….2-27
Parallelogram ……………………………………………………………………………………………2-27
Rhombus ………………………………………………………………………………………………….2-28
Trapezoid………………………………………………………………………………………………….2-28
General Quadrilateral ………………………………………………………………………………..2-28
Theorem………………………………………………………………………………………………………….2-28
Regular Polygon of n Sides Each of Length b……………………………………………….2-28
Circle of radius r ……………………………………………………………………………………….2-28
Regular Polygon of n sides Inscribed in a Circle of Radius r …………………………2-29
Regular Polygon of n Sides Circumscribing a Circle of Radius r …………………..2-29
Cyclic Quadrilateral………………………………………………………………………………………….2-29
Prolemy’s Theorem ………………………………………………………………………………………….2-29
Cyclic-Inscriptable Quadrilateral ………………………………………………………………………2-30
Sector of Circle of Radius r ………………………………………………………………………..2-30
Radius of a Circle Inscribed in a Triangle of Sides a, b, and c ……………………….2-30
Radius of a Circle Circumscribing a Triangle of Sides a, b, and c ………………….2-30
Segment of a Circle of Radius r…………………………………………………………………..2-30
Ellipse of Semimajor Axis a and Semiminor Axis b ……………………………………..2-31
Segment of a Parabola ……………………………………………………………………………….2-31
Planar Areas by Approximation …………………………………………………………………2-31
Solids Bounded By Planes …………………………………………………………………………………2-31
Cube…………………………………………………………………………………………………………2-32
Rectangular Parallelepiped (or Box)……………………………………………………………2-32
Prism………………………………………………………………………………………………………..2-32
Truncated Triangular Prism ………………………………………………………………………2-32
Pyramid ……………………………………………………………………………………………………2-32
Frustum of a Pyramid………………………………………………………………………………..2-33
Prismatoid ………………………………………………………………………………………………..2-33
Regular Polyhedra……………………………………………………………………………………..2-33
Sphere of Radius r ……………………………………………………………………………………..2-34
Right Circular Cylinder of Radius r and Height h………………………………………..2-34
Circular Cylinder of Radius r and Slant Height _………………………………………………..2-35
Cylinder of Cross-Sectional Area A and Slant Height _ ………………………………..2-35
Right Circular Cone of Radius r and Height h …………………………………………….2-35
Spherical Cap of Radius r and Height h ………………………………………………………2-35
Frustum of a Right Circular Cone of Radii a and b and Height h………………….2-35
Zone and Segment of Two Bases ………………………………………………………………..2-35
Lune …………………………………………………………………………………………………………2-36
Spherical Sector…………………………………………………………………………………………2-36
Spherical Triangle and Polygon ………………………………………………………………….2-36
Spheroids…………………………………………………………………………………………………………2-36
Ellipsoid ……………………………………………………………………………………………………2-36
Oblate Spheroid ………………………………………………………………………………………..2-36
Prolate Spheroid………………………………………………………………………………………..2-37
Circular Torus…………………………………………………………………………………………..2-37
Formulas from Plane Analytic Geometry…………………………………………………………..2-37
Distance d between Two Points………………………………………………………………….2-37
Slope m of Line Joining Two Points ……………………………………………………………2-37
Equation of a Line Joining Two Points ……………………………………………………….2-37
Equation of a Line in Terms of x-intercept a _= 0 and y-intercept b _= 0 ……….2-38
Normal Form for Equation of a Line…………………………………………………………..2-38
General Equation of a Line…………………………………………………………………………2-38
Distance From a Point (x1, y1) to the Line Ax +By +C = 0…………………………2-38
Angle ψ between Two Lines Having Slopes m1 and m2 ……………………………….2-38
Area of a Triangle with Vertices …………………………………………………………………2-39
Transformation of Coordinates Involving Pure Translation…………………………2-39
Transformation of Coordinates Involving Pure Rotation …………………………….2-39
Transformation of Coordinates Involving Translation and Rotation…………….2-39
Polar Coordinates (r, θ) ……………………………………………………………………………..2-40
Plane Curves……………………………………………………………………………………………..2-40
Catenary, Hyperbolic Cosine ……………………………………………………………………..2-40
Cardioid ………………………………………………………………………………………………………….2-40
Circle………………………………………………………………………………………………………..2-40
Cassinian Curves……………………………………………………………………………………….2-41
Cotangent Curve………………………………………………………………………………..2-41
Cubical Parabola ………………………………………………………………………………..2-41
Cosecant Curve………………………………………………………………………………….2-41
Cosine Curve……………………………………………………………………………………..2-41
Ellipse ……………………………………………………………………………………………….2-41
Gamma Function……………………………………………………………………………….2-41
Hyperbolic Functions…………………………………………………………………………2-41
Inverse Cosine Curve …………………………………………………………………………2-42
Inverse Sine Curve……………………………………………………………………………..2-42
Inverse Tangent Curve ……………………………………………………………………….2-42
Logarithmic Curve……………………………………………………………………………..2-42
Parabola…………………………………………………………………………………………….2-42
Cubical Parabola ………………………………………………………………………………..2-42
Tangent Curve …………………………………………………………………………………..2-42
Distance d between Two Points…………………………………………………………..2-43
Logarithmic Identities ………………………………………………………………………………………2-46
Series Expansions …………………………………………………………………………………………….2-47
Limiting Values………………………………………………………………………………………………..2-47
Inequalities………………………………………………………………………………………………………2-47
Polynomial Approximations …………………………………………………………………………….2-48
Exponential Function Series Expansion …………………………………………………………….2-49
Fundamental Properties……………………………………………………………………………………2-49
Definition of General Powers ……………………………………………………………………………2-49
Logarithmic and Exponential Functions ……………………………………………………………2-50
Periodic Property ………………………………………………………………………………………2-50
Polynomial Approximations………………………………………………………………………2-50
Slopes ……………………………………………………………………………………………………….2-53
Trigonometric ratios ………………………………………………………………………………………..2-53
Sine Law……………………………………………………………………………………………………2-55
Cosine Law ……………………………………………………………………………………………….2-56
Algebra ……………………………………………………………………………………………………………2-56
Expanding ………………………………………………………………………………………………..2-56
Factoring…………………………………………………………………………………………………..2-57
Roots of a Quadratic Equation ………………………………………………………………………….2-57
Law of exponents ………………………………………………………………………………………2-57
Logarithms ………………………………………………………………………………………………………2-58
3 Statistical Distributions, Methods, and Applications
Discrete Distributions ………………………………………………………………………………………..3-1
Bernoulli Distribution …………………………………………………………………………………3-1
Beta Binomial Distribution ………………………………………………………………………….3-1
Beta Pascal Distribution ………………………………………………………………………………3-3
Binomial Distribution …………………………………………………………………………………3-3
Discrete Weibull Distribution………………………………………………………………………3-3
Geometric Distribution ……………………………………………………………………………….3-3
Hypergeometric Distribution ………………………………………………………………………3-3
Negative Binomial Distribution……………………………………………………………………3-4
Poisson Distribution……………………………………………………………………………………3-4
Rectangular (Discrete Uniform) Distribution ……………………………………………….3-4
Continuous Distributions …………………………………………………………………………………..3-4
Arcsin Distribution……………………………………………………………………………………..3-4
Beta Distribution…………………………………………………………………………………………3-5
Cauchy Distribution ……………………………………………………………………………………3-5
Chi Distribution………………………………………………………………………………………….3-5
Chi-Square Distribution………………………………………………………………………………3-5
Erlang Distribution……………………………………………………………………………………..3-5
Exponential Distribution……………………………………………………………………………..3-6
Extreme-Value Distribution ………………………………………………………………………..3-6
F Distribution …………………………………………………………………………………………….3-6
Gamma Distribution …………………………………………………………………………………..3-7
Half-Normal Distribution ……………………………………………………………………………3-7
Laplace (Double Exponential) Distribution…………………………………………………..3-7
Logistic Distribution……………………………………………………………………………………3-7
Lognormal Distribution ………………………………………………………………………………3-7
Noncentral Chi-Square Distribution…………………………………………………………….3-8
Noncentral F Distribution …………………………………………………………………………..3-8
Noncentral t-Distribution……………………………………………………………………………3-8
Normal Distribution……………………………………………………………………………………3-9
Pareto Distribution ……………………………………………………………………………………..3-9
Rayleigh Distribution ………………………………………………………………………………….3-9
t-Distribution……………………………………………………………………………………………..3-9
Triangular Distribution……………………………………………………………………………..3-10
Uniform Distribution ………………………………………………………………………………..3-10
Weibull Distribution …………………………………………………………………………………3-10
Distribution Parameters …………………………………………………………………………….3-10
Average……………………………………………………………………………………………..3-10
Variance ……………………………………………………………………………………………3-11
Standard Deviation…………………………………………………………………………….3-11
Standard Error …………………………………………………………………………………..3-11
Skewness……………………………………………………………………………………………3-11
Standardized Skewness……………………………………………………………………….3-11
Kurtosis …………………………………………………………………………………………….3-11
Standardized Kurtosis ………………………………………………………………………..3-11
Weighted Average ……………………………………………………………………………..3-11
Estimation and Testing………………………………………………………………………………3-11
100(1−α)% Confidence Interval for Mean…………………………………………..3-11
100(1−α)% Confidence Interval for Variance …………………………………….3-11
100(1−α)% Confidence Interval for Difference in Means ……………………3-12
100(1−α)% Confidence Interval for Ratio of Variances ………………………3-12
Normal Probability Plot …………………………………………………………………………….3-12
Comparison of Poisson Rates …………………………………………………………………….3-13
Distribution Functions—Parameter Estimation ………………………………………….3-13
Bernoulli……………………………………………………………………………………………3-13
Binomial ……………………………………………………………………………………………3-13
Discrete Uniform……………………………………………………………………………….3-13
Geometric………………………………………………………………………………………….3-13
Negative Binomial……………………………………………………………………………………..3-13
Poisson……………………………………………………………………………………………………..3-13
Beta ………………………………………………………………………………………………………….3-14
Chi-Square………………………………………………………………………………………………..3-14
Erlang……………………………………………………………………………………………………….3-14
Exponential ………………………………………………………………………………………………3-14
F Distribution …………………………………………………………………………………………..3-14
Gamma …………………………………………………………………………………………………….3-14
Log–Normal ……………………………………………………………………………………………..3-15
Normal……………………………………………………………………………………………………..3-15
Student’s t …………………………………………………………………………………………………3-15
Triangular…………………………………………………………………………………………………3-15
Uniform……………………………………………………………………………………………………3-15
Weibull …………………………………………………………………………………………………….3-16
Chi-Square Test for Distribution Fitting……………………………………………………..3-16
Kolmogorov–Smirnov Test………………………………………………………………………..3-16
ANOVA ………………………………………………………………………………………………………….3-16
Notation……………………………………………………………………………………………………3-16
Standard Error (Internal) …………………………………………………………………………..3-17
Standard Error (Pooled)…………………………………………………………………………….3-17
Interval Estimates ……………………………………………………………………………………..3-17
Tukey Interval …………………………………………………………………………………………..3-17
Scheffe Interval………………………………………………………………………………………….3-17
Cochran C-Test…………………………………………………………………………………………3-17
Bartlett Test ………………………………………………………………………………………………3-18
Hartley’s Test ……………………………………………………………………………………………3-18
Kruskal–Wallis Test…………………………………………………………………………………..3-18
Adjustment for Ties…………………………………………………………………………………..3-18
Freidman Test …………………………………………………………………………………………..3-18
Regression ………………………………………………………………………………………………..3-19
Notation ……………………………………………………………………………………………3-19
Regression Statistics…………………………………………………………………………………..3-19
Predictions………………………………………………………………………………………………..3-20
Nonlinear Regression ………………………………………………………………………………..3-21
Ridge Regression……………………………………………………………………………………….3-21
Quality Control …………………………………………………………………………………………3-22
For All Quality Control Formulas ……………………………………………………….3-22
Subgroup Statistics…………………………………………………………………………………….3-22
X Bar Charts ……………………………………………………………………………………………..3-22
Capability Ratios ……………………………………………………………………………………….3-23
R Charts……………………………………………………………………………………………………3-24
S Charts…………………………………………………………………………………………………….3-24
C Charts……………………………………………………………………………………………………3-24
U Charts …………………………………………………………………………………………………..3-24
P Charts ……………………………………………………………………………………………………3-24
NP Charts …………………………………………………………………………………………………3-25
CuSum Chart for the Mean………………………………………………………………………..3-25
Multivariate Control Charts……………………………………………………………………….3-25
Time-Series Analysis …………………………………………………………………………………3-25
Notation ……………………………………………………………………………………………3-25
Autocorrelation at Lag k…………………………………………………………………………….3-26
Partial Autocorrelation at Lag k………………………………………………………………….3-26
Cross-Correlation at Lag k …………………………………………………………………………3-26
Box-Cox……………………………………………………………………………………………………3-26
Periodogram (computed using Fast Fourier Transform) ……………………………..3-27
Categorical Analysis ………………………………………………………………………………….3-27
Notation ……………………………………………………………………………………………3-27
Totals ……………………………………………………………………………………………………….3-27
Chi-Square………………………………………………………………………………………………..3-27
Fisher’s Exact Test …………………………………………………………………………………….3-28
Lambda…………………………………………………………………………………………………….3-28
Uncertainty Coefficient ……………………………………………………………………………..3-28
Somer’s D …………………………………………………………………………………………………3-29
Eta ……………………………………………………………………………………………………………3-29
Contingency Coefficient…………………………………………………………………………….3-30
Cramer’s V ……………………………………………………………………………………………….3-30
Conditional Gamma………………………………………………………………………………….3-30
Pearson’s R ……………………………………………………………………………………………….3-30
Kendall’s Tau b………………………………………………………………………………………….3-30
Tau C ……………………………………………………………………………………………………….3-30
Probability Terminology ……………………………………………………………………………3-30
Basic Probability Principles………………………………………………………………………..3-31
Random Variable ………………………………………………………………………………………3-31
Mean Value ˆx or Expected Value μ…………………………………………………………….3-31
Discrete Distribution Formulas ………………………………………………………………….3-32
Bernoulli Distribution ……………………………………………………………………………….3-32
Beta Binomial Distribution ………………………………………………………………………..3-32
Beta Pascal Distribution …………………………………………………………………………….3-32
Binomial Distribution ……………………………………………………………………………….3-32
Discrete Weibull Distribution…………………………………………………………………….3-32
Geometric Distribution ……………………………………………………………………………..3-33
Hypergeometric Distribution …………………………………………………………………….3-33
Negative Binomial Distribution………………………………………………………………….3-33
Poisson Distribution………………………………………………………………………………….3-34
Rectangular (Discrete Uniform) Distribution ……………………………………………..3-34
Continuous Distribution Formulas …………………………………………………………….3-34
Arcsin Distribution……………………………………………………………………………………3-34
Beta Distribution……………………………………………………………………………………….3-35
Cauchy Distribution ………………………………………………………………………………….3-35
Chi Distribution………………………………………………………………………………………..3-35
Chi-Square Distribution…………………………………………………………………………….3-35
Erlang Distribution……………………………………………………………………………………3-35
Exponential Distribution……………………………………………………………………………3-35
Extreme-Value Distribution ………………………………………………………………………3-36
F Distribution …………………………………………………………………………………………..3-36
Gamma Distribution …………………………………………………………………………………3-36
Half-Normal Distribution ………………………………………………………………………….3-36
Laplace (Double Exponential) Distribution…………………………………………………3-37
Logistic Distribution………………………………………………………………………………….3-37
Lognormal Distribution …………………………………………………………………………….3-37
Noncentral Chi-Square Distribution…………………………………………………………..3-37
Noncentral F Distribution …………………………………………………………………………3-38
Noncentral t-Distribution………………………………………………………………………….3-38
Normal Distribution………………………………………………………………………………….3-38
Pareto Distribution ……………………………………………………………………………………3-38
Rayleigh Distribution ………………………………………………………………………………..3-39
t-Distribution……………………………………………………………………………………………3-39
Triangular Distribution……………………………………………………………………………..3-39
Uniform Distribution ………………………………………………………………………………..3-39
Weibull Distribution …………………………………………………………………………………3-40
Variate Generation Techniques…………………………………………………………………………3-40
Notation……………………………………………………………………………………………………3-40
Variate Generation Algorithms …………………………………………………………………………3-40
References ……………………………………………………………………………………………………….3-42
4 Computations with Descriptive Statistics
Sample Average …………………………………………………………………………………………………4-1
Application Areas ……………………………………………………………………………………….4-1
Sample calculations……………………………………………………………………………………..4-1
Sample Variance ………………………………………………………………………………………………..4-1
Application Areas ……………………………………………………………………………………….4-1
Sample Calculations…………………………………………………………………………………….4-2
Sample Standard Deviation…………………………………………………………………………………4-2
Application Areas ……………………………………………………………………………………….4-2
Sample Standard Error of the Mean…………………………………………………………………….4-3
Application Areas ……………………………………………………………………………………….4-3
Skewness…………………………………………………………………………………………………….4-3
Standardized Skewness………………………………………………………………………………..4-3
Kurtosis………………………………………………………………………………………………………4-4
Standardized Kurtosis………………………………………………………………………………….4-4
Weighted Average……………………………………………………………………………………….4-4
Estimation and Testing ………………………………………………………………………………………4-4
100(1−α)% Confidence Interval for Mean…………………………………………………..4-4
100(1−α)% Confidence Interval for Variance ……………………………………………..4-4
100(1−α)% Confidence Interval for Difference
in Means………………………………………………………………………………………4-4
100(1−α)% Confidence Interval for Ratio
of Variances………………………………………………………………………………….4-5
Normal Probability Plot ………………………………………………………………………………4-5
Comparison of Poisson Rates ………………………………………………………………………4-5
Distribution Functions and Parameter Estimation……………………………………………….4-5
Bernoulli Distribution …………………………………………………………………………………4-5
Binomial Distribution …………………………………………………………………………………4-5
Discrete Uniform Distribution …………………………………………………………………….4-6
Geometric Distribution ……………………………………………………………………………….4-6
Negative Binomial Distribution……………………………………………………………………4-6
Poisson Distribution……………………………………………………………………………………4-6
Beta Distribution…………………………………………………………………………………………4-6
Chi-Square Distribution………………………………………………………………………………4-6
Erlang Distribution……………………………………………………………………………………..4-6
Exponential Distribution……………………………………………………………………………..4-7
Application Areas ………………………………………………………………………………..4-7
F Distribution …………………………………………………………………………………………….4-7
Gamma Distribution …………………………………………………………………………………..4-7
Log–Normal Distribution ……………………………………………………………………………4-7
Normal Distribution……………………………………………………………………………………4-8
Triangular Distribution……………………………………………………………………………….4-8
Uniform Distribution ………………………………………………………………………………….4-8
Weibull Distribution …………………………………………………………………………………..4-8
Chi-Square Test for Distribution Fitting……………………………………………………….4-8
Kolmogorov–Smirnov Test………………………………………………………………………….4-9
ANOVA ……………………………………………………………………………………………4-9
Notation……………………………………………………………………………………………………..4-9
Standard Error ……………………………………………………………………………………………4-9
Interval Estimates ……………………………………………………………………………………….4-9
Tukey Interval …………………………………………………………………………………………..4-10
Scheffe Interval………………………………………………………………………………………….4-10
Cochran C-test ………………………………………………………………………………………….4-10
Bartlett Test ………………………………………………………………………………………………4-10
Hartley’s Test ……………………………………………………………………………………………4-10
Kruskal–Wallis Test…………………………………………………………………………………..4-11
Adjustment for ties …………………………………………………………………………….4-11
Freidman Test …………………………………………………………………………………………..4-11
Regression …………………………………………………………………………………………………4-12
Notation……………………………………………………………………………………………………4-12
Statistical Quality Control…………………………………………………………………………………4-13
Subgroup Statistics…………………………………………………………………………………….4-13
X-Bar Charts …………………………………………………………………………………………….4-14
Capability Ratios ……………………………………………………………………………………….4-14
R Charts……………………………………………………………………………………………………4-15
S Charts…………………………………………………………………………………………………….4-15
C Charts……………………………………………………………………………………………………4-15
U Charts …………………………………………………………………………………………………..4-15
P Charts ……………………………………………………………………………………………………4-15
NP Charts …………………………………………………………………………………………………4-16
CuSum Chart for the Mean………………………………………………………………………..4-16
Time-Series Analysis …………………………………………………………………………………4-16
Notation……………………………………………………………………………………………………4-16
Autocorrelation at Lag k…………………………………………………………………………….4-17
Partial Autocorrelation at Lag k………………………………………………………………….4-17
Cross-Correlation at Lag k …………………………………………………………………………4-17
Box-Cox Computation ………………………………………………………………………………4-17
Periodogram (Computed using Fast Fourier
Transform)…………………………………………………………………………………4-18
Categorical Analysis …………………………………………………………………………4-18
Notation……………………………………………………………………………………………………4-18
Totals ……………………………………………………………………………………………………….4-18
Chi-Square………………………………………………………………………………………………..4-18
Lambda…………………………………………………………………………………………………….4-19
Uncertainty Coefficient ……………………………………………………………………………..4-19
Somer’s D Measure……………………………………………………………………………………4-20
Eta ……………………………………………………………………………………………………………4-20
Contingency Coefficient…………………………………………………………………………….4-21
Cramer’s V Measure ………………………………………………………………………………….4-21
Conditional Gamma………………………………………………………………………………….4-21
Pearson’s R Measure………………………………………………………………………………….4-21
Kendall’s Tau b Measure ……………………………………………………………………………4-21
Tau C Measure………………………………………………………………………………………….4-22
Overall Mean…………………………………………………………………………………………….4-22
Chebyshev’s Theorem ……………………………………………………………………………….4-22
Permutation ……………………………………………………………………………………………..4-22
Combination …………………………………………………………………………………………….4-22
Failure ………………………………………………………………………………………………………4-22
5 Computations for Economic Analysis
Fundamentals of Economic Analysis …………………………………………………………5-1
Simple Interest ……………………………………………………………………………………………5-1
Future value…………………………………………………………………………………………5-1
Compound Interest …………………………………………………………………………………….5-2
Continuous Compound Interest …………………………………………………………..5-2
Effective Rate……………………………………………………………………………………….5-3
Present Value with Compound Interest…………………………………………………5-3
Annuities ……………………………………………………………………………………………………5-4
Present value of annuity ……………………………………………………………………….5-4
Future value of an annuity ……………………………………………………………………5-4
Amortization of Loans…………………………………………………………………………………5-5
Interest and Equity Computations ………………………………………………………………………5-5
Equity Break-Even Formula ……………………………………………………………………………….5-8
Sinking Fund Payment ………………………………………………………………………………..5-9
Internal Rate of Return…………………………………………………………………………5-9
Benefit–Cost Ratio……………………………………………………………………………….5-9
Simple Payback Period …………………………………………………………………………5-9
Discounted Payback Period ………………………………………………………………..5-10
Economic Methods of Comparing Investment Alternatives…………………………5-10
Present Value Analysis ………………………………………………………………………………5-10
Annual Value Analysis ………………………………………………………………………………5-10
Internal Rate of Return Analysis…………………………………………………………………5-11
External Rate of Return Analysis ………………………………………………………………..5-11
Incremental Analysis………………………………………………………………………………….5-11
Guidelines for Comparison of
Alternatives ………………………………………………………………………………..5-12
Asset Replacement and Retention Analysis………………………………………………………..5-12
Replacement Analysis Computation………………………………………………………………….5-14
Depreciation Methods………………………………………………………………………………………5-15
Depreciation Terminology………………………………………………………………………………..5-15
Depreciation Methods……………………………………………………………………………….5-16
Straight-Line (SL) Method …………………………………………………………………………5-16
Declining Balance (DB) Method…………………………………………………………………5-16
Sums-of-Years’ Digits (SYD) Method…………………………………………………………5-17
MACRS Method ……………………………………………………………………………………….5-17
Effects of Inflation and Taxes……………………………………………………………………..5-18
Foreign Exchange Rates……………………………………………………………………………..5-21
After-Tax Economic Analysis …………………………………………………………………….5-21
Cost and Value Computations …………………………………………………….5-22
Actual Cost of Work Performed…………………………………………………………………5-23
Applied Direct Cost …………………………………………………………………………………..5-23
Budgeted Cost for Work Performed……………………………………………………………5-23
Budgeted Cost for Work Scheduled ……………………………………………………………5-23
Direct Cost ……………………………………………………………………………………………….5-23
Economies of Scale ……………………………………………………………………………………5-23
Estimated Cost at Completion ……………………………………………………………………5-23
First Cost ………………………………………………………………………………………………….5-24
Fixed Cost…………………………………………………………………………………………………5-24
Incremental Cost……………………………………………………………………………………….5-24
Indirect Cost……………………………………………………………………………………………..5-24
Life-Cycle Cost………………………………………………………………………………………….5-24
Maintenance Cost ……………………………………………………………………………………..5-24
Marginal Cost……………………………………………………………………………………………5-24
Operating Cost………………………………………………………………………………………….5-24
Opportunity Cost………………………………………………………………………………………5-25
Overhead Cost…………………………………………………………………………………………..5-25
Standard Cost……………………………………………………………………………………………5-25
Sunk Cost …………………………………………………………………………………………………5-25
Total Cost …………………………………………………………………………………………………5-25
Variable cost……………………………………………………………………………………………..5-25
Cash-Flow Calculations …………………………………………………………………….5-26
Calculations with Compound Amount Factor …………………………………………….5-26
Calculations with Present Worth Factor……………………………………………………..5-27
Calculations with Uniform Series Present Worth Factor ……………………………..5-27
Calculations with Uniform Series Capital Recovery Factor…………………………..5-28
Calculations with Uniform Series Compound Amount Factor……………………..5-29
Calculations with Uniform Series Sinking Fund Factor ……………………………….5-29
Calculations with Capitalized Cost Formula ……………………………………………….5-30
Arithmetic Gradient Series…………………………………………………………………………5-31
Internal Rate of Return………………………………………………………………………………5-32
Benefit-Cost Ratio Analysis………………………………………………………………………..5-33
Simple Payback Period ………………………………………………………………………………5-33
Discounted Payback Period ……………………………………………………………………….5-34
Time Required to Double Investment…………………………………………………………5-35
Effects of Inflation on Industrial Project Costing…………………………………………5-36
Mild Inflation ……………………………………………………………………………………………5-40
Moderate Inflation…………………………………………………………………………………….5-40
Severe Inflation …………………………………………………………………………………………5-40
Hyperinflation…………………………………………………………………………………………..5-40
Break-Even Analysis ………………………………………………………………………………….5-40
Profit Ratio Analysis…………………………………………………………………………..5-42
Project Cost Estimation ……………………………………………………………………5-46
Optimistic and Pessimistic Cost Estimates ………………………………………………….5-47
Cost Performance Index ………………………………………………………………5-47
Cost Control Limits……………………………………………………………………..5-48
Project Balance Computation……………………………………………………………..5-48

This book is US$10. Order for this book:
(Request for sample page click on "Order Now" button)

Book Order
Or, Send email: textileebooks@gmail.com

Share this Book!

Leave a Comment