Handbook of Industrial Engineering Equations, Formulas, and Calculations

Handbook of Industrial Engineering Equations, Formulas, and Calculations
اسم المؤلف
Adedeji B. Badiru, Olufemi A.Omitaomu
التاريخ
3 يناير 2018
المشاهدات
التقييم
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Handbook of Industrial Engineering Equations, Formulas, and Calculations
Adedeji B. Badiru
Olufemi A.Omitaomu
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
ixx Contents
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 xˆ 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 2-20Contents xi
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 2-32xii Contents
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 2-41Contents xiii
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 .3-3xiv Contents
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 .3-12Contents xv
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 3-22xvi Contents
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 xˆ 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 .3-33Contents xvii
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 .4-3xviii Contents
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 4-10Contents xix
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 .4-22xx Contents
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 .5-23Contents xxi
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 .5-48xxii Contents
6 Industrial Production Calculations
Learning Curve Models and Computations 6-1
The Average Cost Model .6-1
Computational Example 6-2
Computational Example 6-3
The Unit Cost Model .6-4
Productivity Calculations Using Learning Curves 6-5
Determining Average Unit Time 6-5
Calculation of the Learning Factor .6-5
Calculating Total Time for a Job .6-5
Time Required to Perform a Task for the nth Time 6-5
The Improvement Ratio 6-5
Computational Example 6-5
Solution 6-5
Computation for Improvement Goal in Unit Time 6-6
Computation of Machine Output Capacities .6-6
Machine Utilization Ratio: Determining How Often a
Machine Is Idle 6-6
Calculating Number of Machines Needed to Meet Output 6-7
Alternate Forms for Machine Formula 6-7
Calculating Buffer Production to Allow for Defects .6-8
Adjusting Machine Requirements to Allow for Rejects 6-9
Output Computations for Sequence of Machines .6-9
Calculating Forces on Cutting Tools 6-10
Calculating Pressure 6-11
Finding Required Horsepower .6-11
Machine Accuracy .6-12
Calculating the Goal Dimension .6-12
Drill Thrust 6-13
Drill Torque .6-14
Drill Horsepower .6-14
Calculating Speed and Rotation of Machines 6-14
Shaft Speed .6-15
Surface Speed .6-15
Tool Feed per Revolution 6-16
Tool Feed per Minute 6-16
Tool Feed per Tooth 6-17
Computation to Find the Volume of Material Removed 6-17
Time Rate for Material Removal in a Rectangular Cut .6-17
Calculation of Linear Feed for Rectangular Material Removal 6-18
Takt Time for Production Planning .6-18
Production Crew Work Rate Analysis .6-19
Production Work Rate Example .6-20Contents xxiii
Case of Multiple Resources Working Together .6-20
Computational Examples 6-21
Calculation of Personnel Requirements .6-22
Calculation of Machine Requirements .6-23
References 6-23
7 Forecasting Calculations
Forecasting Based on Averages .7-1
Simple Average Forecast .7-1
Period Moving Average Forecast 7-2
Weighted Average Forecast .7-2
Weighted T-Period Moving Average Forecast 7-2
Exponential Smoothing Forecast 7-3
Regression Analysis .7-3
Regression Relationships .7-3
Prediction .7-4
Control .7-4
Procedure for Regression Analysis .7-5
Coefficient of Determination 7-5
Residual Analysis .7-7
Time-Series Analysis .7-9
Stationarity and Data Transformation .7-10
Moving Average Processes 7-12
Autoregressive Processes .7-13
Forecasting for Inventory Control 7-15
Economic Order Quantity Model .7-15
Quantity Discount .7-16
Calculation of Total Relevant Cost .7-16
Evaluation of the Discount Option .7-17
Sensitivity Analysis 7-19
Wagner–Whitin Algorithm 7-20
Notation and Variables 7-21
8 Six Sigma and Lean
Concept of Six Sigma .8-1
Taguchi Loss Function 8-1
Identification and Elimination of Sources of Defects 8-2
Roles and Responsibilities for Six Sigma 8-3
Statistical Techniques for Six Sigma .8-3
Control Charts .8-4
X and R-Charts 8-4
Data Collection Strategies .8-5
Subgroup Sample Size .8-5
Frequency of Sampling 8-6xxiv Contents
Stable Process .8-6
Out-of-Control Patterns 8-6
Calculation of Control Limits .8-7
Plotting Control Charts for Range and Average Charts 8-8
Plotting Control Charts for Moving Range and Individual
Control Charts .8-9
Case Example: Plotting of Control Chart .8-9
Calculations 8-9
Trend Analysis .8-14
Process Capability Analysis for Six Sigma .8-18
Capable Process (Cp) .8-18
Capability Index (Cpk) .8-19
Process Capability Example 8-20
Possible Applications of Process Capability Index 8-21
Potential Abuse of C
p and Cpk .8-22
Lean Principles and Applications .8-22
Kaizen of a Process 8-23
Lean Task Value Rating System 8-24
9 Risk Computations
Cost Uncertainties .9-1
Schedule Uncertainties 9-2
Performance Uncertainties .9-2
Decision Tables and Trees 9-2
Reliability Calculations 9-7
General Reliability Definitions 9-8
Exponential Distribution Used as Reliability
Function .9-9
Reliability Formulas .9-10
General Reliability Definitions 9-10
Exponential Distribution Used as Reliability
Function .9-11
10 Computations for Project Analysis
Planning .10-1
Organizing .10-1
Scheduling 10-1
Control .10-2
CPM Scheduling 10-2
Advantages for Communication .10-3
Advantages for Control .10-3
Advantages for Team Interaction .10-3
Activity Precedence Relationships .10-4
Network Notation 10-4Contents xxv
Forward-Pass Calculations 10-5
CPM Example 10-6
Backward-Pass Calculations .10-7
Calculation of Slacks .10-8
Calculations for Subcritical Paths 10-9
Plotting of Gantt Charts 10-10
Calculations for Project Crashing 10-13
Calculations for Project Duration Diagnostics 10-18
PERT Formulas .10-19
Activity Time Distributions 10-19
Project Duration Analysis .10-20
Simulation of Project Networks 10-24
11 Product Shape and Geometrical Calculations
Equation of a Straight Line .11-1
Quadratic Equation .11-2
Conic Sections .11-2
Case 1 of Conic Section: e = 1 (Parabola) 11-3
Case 2 of Conic Section: e < 1 (Ellipse) .11-3 Case 3 Hyperbola: e > 1 11-4
Case 4 e = 1 (Circle) 11-5
Conic Section Equation 11-6
Quadric Surface (Sphere) 11-6
Identities .11-7
Trigonometry .11-7
Law of Sines 11-7
Law of Cosines .11-8
Identities .11-8
Complex Numbers .11-10
Polar Coordinates 11-10
Euler’s Identity .11-11
Roots .11-11
Matrices 11-11
Matrix Multiplication 11-11
Matrix Addition .11-11
Identity Matrix .11-11
Matrix Transpose .11-11
Matrix Inverse 11-12
Determinants .11-12
Vectors .11-12
Gradient, Divergence, and Curl 11-13
Identities .11-13
Progressions and Series .11-14
Arithmetic Progression .11-14xxvi Contents
Geometric Progression 11-14
Properties of Series 11-15
Power Series .11-15
Taylor’s Series 11-16
Differential Calculus .11-16
The Derivative 11-16
Test for a Maximum 11-16
Test for a Minimum 11-16
Test for a Point of Inflection .11-16
The Partial Derivative 11-16
Curvature in Rectangular Coordinates 11-17
The Radius of Curvature .11-17
L’Hospital’s Rule 11-17
Integral Calculus 11-18
Derivatives and Indefinite Integrals .11-18
Derivatives .11-18
Indefinite Integrals .11-20
Mensuration of Areas and Volumes 11-21
Nomenclature 11-21
Parabola 11-21
Ellipse 11-21
Circular Segment .11-22
Circular Sector .11-22
Sphere .11-22
Parallelogram .11-22
Regular Polygon (n Equal Sides) .11-23
Prismoid .11-23
Right Circular Cone .11-23
Right Circular Cylinder .11-23
Paraboloid of Revolution .11-23
Centroids and Moments of Inertia .11-24
Difference Equations .11-24
First-Order Linear Difference Equation .11-25
Second-Order Linear Difference Equation 11-25
Numerical Methods .11-25
Newton’s Method for Root Extraction .11-25
Newton’s Method of Minimization 11-25
Numerical Integration .11-26
Euler’s or Forward Rectangular Rule .11-26
Trapezoidal Rule 11-26
Simpson’s Rule/Parabolic Rule (n Must Be
an Even Integer) 11-27
Calculation of Best-Fit Circle .11-27Contents xxvii
12 General Engineering Calculations
Six Simple Machines for Materials Handling 12-1
Machine 1: The Lever 12-1
Machine 2: Wheel and Axle 12-1
Machine 3: The Pulley .12-2
Machine 4: The Inclined Plane .12-2
Machine 5: The Wedge 12-2
Machine 6: The Screw 12-2
Mechanics: Kinematics .12-3
Scalars and Vectors 12-3
Distance and Displacement .12-3
Acceleration .12-3
Speed and Velocity 12-3
Frequency .12-3
Period .12-3
Angular Displacement .12-3
Angular Velocity 12-4
Angular Acceleration .12-4
Rotational Speed 12-4
Uniform Linear Motion 12-4
Uniform Accelerated Linear Motion 12-4
Rotational Motion .12-5
Uniform Rotation and a Fixed Axis .12-5
Uniform Accelerated Rotation about a Fixed Axis 12-5
Simple Harmonic Motion .12-6
Pendulum .12-7
Free Fall 12-7
Vertical Project 12-7
Angled Projections .12-8
Horizontal Projection (α = 0) .12-8
Sliding Motion on an Inclined Plane 12-8
Rolling Motion on an Inclined Plane .12-9
Mechanics: Dynamics .12-10
Newton’s First Law of Motion 12-10
Newton’s Second Law of Motion 12-10
Newton’s Third Law of Motion 12-10
Momentum of Force 12-10
Impulse of Force 12-11
Law of Conservation of Momentum 12-11
Friction .12-11
General Law of Gravity .12-11
Gravitational Force 12-12
Centrifugal Force .12-12
Centripetal Force .12-12xxviii Contents
Torque 12-12
Work .12-13
Energy .12-13
Conservation of Energy .12-14
Power 12-14
Appendix A: Mathematical Patterns, Series, and Formulae
Number Sequence and Patterns A-1
Closed-Form Mathematical Expressions A-3
Derivation of the Quadratic Formula A-7
Appendix B: Measurement Units, Notation, and Constants
Common Notation . B-1
Scientific Constants B-3
Numbers and Prefixes B-3
Appendix C: Conversion Factors
Area Conversion Factors C-1
Volume Conversion Factors C-2
Energy Conversion Factors C-2
Mass Conversion Factors . C-3
Temperature Conversion Factors C-3
Velocity Conversion Factors C-4
Pressure Conversion Factors . C-4
Distance Conversion Factors . C-5
Physical Science Equations C-6
English and Metric Systems . C-7
Household Measurement Conversion C-7
Appendix D: Factors and Tables
Formulas for Interest Factor D-1
Summation Formulas for Closed-Form Expressions .D-3
Interest Tables .D-3
Appendix E: Greek Symbols and Roman Numerals
Greek Symbols E-1
Roman Numerals E-2
Bibliography . Bibliography-1
Index Index-1
Index
A
Acceleration(s), 12-3. See also Newton’s
laws of motion; Velocity
angular, 12-4, 12-6
centripetal, 12-5
falling body, 12-12
inclined plane, 12-8, 12-9
Newton’s second law, 12-10
tangential, 12-5
Acre, 2-59, B-1, C-7
Action and reaction, law of, 12-10. See also
Newton’s laws of motion
Activity, 10-3
antecedent, 10-4
descendent, 10-4
expected duration, 10-19
predecessor, 10-4
successor, 10-4
time distributions, 10-19
time modeling, 10-25
variance, 10-19
Activity duration (t), 10-18–19
crashing, 10-13
probabilistic properties modeling, 10-19
Activity-on-arrow (AOA), 10-2. See also
Activity-on-node (AON)
Activity-on-node (AON), 10-2, 10-6
graphical representation, 10-4
network components, 10-3, 10-4
Activity precedence relationships, 10-4
backward-pass calculations, 10-7
CPM example, 10-6
dummy activities, 10-6
forward-pass calculations, 10-5
network notation, 10-4
adjusted coefficient of multiple determination,
7-6. See also Determination
coefficient
ADR. See Asset depreciation range (ADR)
ADS. See Alternate Depreciation System (ADS)
AFL. See American Federation of Labor (AFL)
After-tax economic analysis
after-tax MARR, 5-22
tax types, 5-21
taxable income equation, 5-22
Agate, B-1
Algebra
arithmetic mean, 2-20
arithmetic progression, 2-20
expanding, 2-56
factoring, 2-57
geometric mean, 2-20
geometric progression, 2-20
harmonic mean, 2-20
operations laws, 2-17
powers and roots, 2-19
proportions, 2-19
special products and factors, 2-17–18
Alternate Depreciation System (ADS), 5-17
American Federation of Labor (AFL), 1-11
American Society of Mechanical Engineers
(ASME), 1-11
Ampere, B-1
Amplitude, 12-6
Analysis of variance (ANOVA), 7-3
adjustment for ties, 3-18, 4-11
Bartlett test, 3-18, 4-10
Cochran C-test, 3-17, 4-10
Freidman test, 3-18–19, 4-11
Hartley’s test, 3-18, 4-10
interval estimates, 4-9
Kruskal-Wallis test, 3-18, 4-11
notation, 3-16, 4-9
Scheffe interval, 3-17, 4-10
standard error, 3-17, 4-9
Tukey interval, 3-17, 4-10
Angled projections, 12-8
Angular
acceleration, 12-4, 12-6
displacement, 12-3
velocity, 12-4, 12-5, 12-6
Index-1Index-2 Index
Annuity, 5-4, 5-10
future value, 5-4–5
present value, 5-4
ANOVA. See Analysis of variance (ANOVA)
Antecedent activity, 10-4
AOA. See Activity-on-arrow (AOA)
AON. See Activity-on-node (AON)
Arcsin distribution, 3-4, 3-34
Arithmetic progression, 2-14, 2-20, 11-14
Arithmetic sequence. See Arithmetic
progression
AR process. See Autoregressive (AR) processes
Arrow, 10-3
ASME. See American Society of Mechanical
Engineers (ASME)
Asset depreciation, 5-15
book depreciation, 5-15
book value, 5-15
DB method, 5-16–17
first cost, 5-15
half-year convention, 5-16, 5-20
MACRS method, 5-17–19
market value, 5-16
real property, 5-20
recovery period, 5-16
recovery rate, 5-16
requirements, 5-15
salvage value, 5-15
SL method, 5-16
SYD method, 5-17
tax depreciation, 5-15
Asset depreciation range (ADR), 5-18
Asset replacement analysis
asset life, 5-13
challenger, 5-13
challenger first cost, 5-13
computational process, 4-14–15
defender, 5-13
deteriorating factor, 5-12
financial factor, 5-13
first cost, 5-13
marginal cost, 5-14
outsider viewpoint, 5-13
requirements factor, 5-13
tax analysis, 5-14
technological factor, 5-13
Associative law, 2-9, 2-17
Astronomical unit (A.U.), B-2
Autocorrelation, 3-26, 4-17, 7-12
function, 7-10
partial, 3-26, 4-17
sample, 7-12
theoretical, 7-12
Autocovariances, 7-12. See also Covariance
Autoregressive (AR) processes, 7-13
Average, 3-10, 4-1
application areas, 4-1
calculations, 4-1
forecasting, 7-1–3
treatment rank, 3-18, 4-11
unit time, 6-5
weighted, 3-11, 4-4
Average cost model, 6-1, 6-4
learning curve exponent, 6-1
log–log paper, 6-2
percent productivity gain, 6-2
Average to date, 7-1–2. See also Forecasting
Average unit time determination, 6-5
B
Backward-pass calculations, 10-7. See also
Forward-pass calculations
Bale, B-2
Bartlett test, 3-18, 4-10
Bernoulli distribution. See Binomial
distribution
Best-fit circle, 11-27, 11-28
co-ordinate system, 11-29
normal equations, 11-28–29
variance, 11-27
Beta binomial distribution, 3-1, 3-32
Beta distribution, 3-5, 3-35, 4-6, 10-20. See also
Triangular—probability density
function
Beta Pascal distribution, 3-3, 3-32
Binomial distribution, 2-5, 3-3, 3-32, 4-5.
See also Probability distribution
beta, 3-1, 3-32
cumulative function, 2-6
mean, 2-6
negative, 3-4, 3-33, 4-6
normal distribution, 2-6
Poisson distribution, 2-5
population mean, 2-6
variance, 2-6
Binomial theorem, 2-14
Black belt, 8-3
Board foot, B-2
Bolt, B-2
Break-even analysis, 5-40
multiple projects, 5-42Index Index-3
profit due, 5-41
single project, 5-41
total revenue, 5-41
Bridge proposals, 1-4
Btu, B-2
Buffer production calculation, 6-8–9
Burst point, 10-4
C
Calling population, 1-17
Capability, 8-18. See also Process
capability analysis
Capability index, 8-19, 8-21
applications, 8-21–22
capable but not centered process, 8-20
centered and capable process, 8-20
centered but not capable process, 8-21
Capable process, 8-18–19
Carat, B-2. See also Karat
Cardinal scale, 1-23
Cardioid, 2-40
Cash-flow calculations, 5-26
arithmetic gradient series, 5-31–32
benefit-cost ratio analysis, 5-33
break-even analysis, 5-40–42
capital recovery factor, 5-28, 5-29
capitalized cost cash flow, 5-30
capitalized cost formula, 5-30, 5-31
compound amount cash flow, 5-29
compound amount factor, 5-26, 5-29
discounted payback period, 5-34–35
inflation, 5-36–40
IRR, 5-32–33
MARR, 5-26
notation, 5-26
payback period, 5-33–34
present worth factor, 5-27–28
profit ratio analysis, 5-42–46
project balance computation, 5-48
project cost estimation, 5-46–48
Rule of 72 evaluation, 5-36, 5-37
single-payment, 5-27
sinking fund factor, 5-29–30
time required, 5-35, 5-36
uniform series cash flow, 5-27
Cassinian curves, 2-41–42
Categorical analysis
Chebyshev’s theorem, 4-22
Chi-square, 3-27, 4-18
combination, 4-22
conditional gamma, 3-30, 4-21
contingency coefficient, 3-30, 4-21
Cramer’s V measure, 3-30, 4-21
Eta, 3-29, 4-20–21
failure, 4-22
Fisher’s exact test, 3-28
Kendall’s Tau b measure, 3-30, 4-21
Lambda, 3-28, 4-19
notation, 3-27, 4-18
overall mean, 4-22
Pearson’s R measure, 3-30, 4-21
permutation, 4-22
Somer’s D measure, 3-29, 4-20
Tau C, 3-30, 4-22
totals, 3-27, 4-18
uncertainty coefficient, 3-28, 4-19
Catenary, 2-40
Cauchy distribution, 3-5, 3-35
Center lines, 8-7
Centrifugal force, 12-12
Centripetal force, 12-12. See also
Centrifugal force
Centroidal moment of inertia, 11-24
Centroids, 11-24
Ceva’s theorem, 2-27
Chain, B-2
Chebyshev’s theorem, 2-2, 4-22
Chi distribution, 3-5, 3-35
Chi-square, 2-27, 3-14, 3-27, 4-6, 4-18
Chi-square test, 3-16, 4-8
Chi-squared, 2-7
Circle, 2-40, 11-5
radius, 2-28
sector formula, 2-30
tangent length, 11-5
Circular
sector, 11-22
segment, 11-22
torus, 2-37
Circular cone, right, 2-35, 11-23
Circular cylinder, 2-35
formulas, 2-35
right, 2-34, 11-23
Closed-form expressions, A-3
common forms, A-4
derivation, A-7
summation formulas, D-3
CMMs. See Coordinate measuring machines
(CMMs)
Cochran C-test, 3-17, 4-10
Commutative law, 2-9, 2-17Index-4 Index
Complex numbers, 11-10
Compound interest, 5-2
continuous, 5-2
effective rate, 5-3
present value, 5-3–4
Computational analysis, 1-22
cardinal scale, 1-22
interval scale, 1-22
nominal scale, 1-22
ordinal scale, 1-22
ratio scale, 1-22
Computer simulation, 10-24
activity time modeling, 10-25
project analysis, 10-25
Cone, 2-35
right circular, 11-23
surface area, 2-35, 2-52
volume, 2-35, 2-52
Conic section(s), 11-2
circle, 11-5
ellipse, 11-3, 11-4
equations, 11-6
hyperbola, 11-4
parabola, 11-3
plot, 11-2
Conservation of energy, 12-14
Conservation of momentum, law of, 12-11
Control charts, 8-4, 8-9–14
attribute data, 8-4
constants, 8-8
moving range and individual charts, 8-9
multivariate, 3-25
range and average charts, 8-8
trend analysis, 8-14–18
variable data, 8-4
Conversion factor, C-1
area, C-1
distance, C-5
energy, C-2
mass, C-3
pressure, C-4
temperature, C-3
velocity, C-4
volume, C-2
Coordinate measuring machines
(CMMs), 11-27
Correlation coefficient, 7-10, 7-11
Cosine formula. See Cosine law
Cosine law, 2-56, 11-8
Cosine rule. See Cosine law
Cost and value computations, 5-22
actual cost, 5-23
budgeted cost, 5-23
direct cost, 5-23
estimated cost, 5-23
first cost, 5-24
fixed cost, 5-24
incremental 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
Cost performance index (CPI), 5-47
Cost/schedule control systems criteria
(C/SCSC), 6-21
Cost uncertainties, 9-1
Covariance, 7-10. See also Variance
sample estimates, 7-12
theoretical, 7-11
CPI. See Cost performance index (CPI)
CPM. See Critical Path Method (CPM)
Cramer’s Vmeasure, 3-30, 4-21
Crashing ratios, 10-17, 10-18
Crash task duration, 10-15
crash cost, 10-16
CRD. See Critical Resource
Diagramming (CRD)
Crew size, 6-19
Critical activities, 10-8, 10-9, 10-18
Criticality level, 10-10
Critical path, 10-8
activity slack types, 10-8
sequence of activities, 10-9
Critical Path Method (CPM), 9-3, 10-2, 10-6.
See also Program Evaluation and
Review Technique (PERT)
advantages, 10-3
backward-pass analysis, 10-7
crashing options, 10-18
forward-pass analysis, 10-7
fully crashed CPM network, 10-16
network control, 10-3
network planning, 10-2
network scheduling phase, 10-3
network with deadline, 10-10Index Index-5
sample project, 10-6, 10-9
scheduling, 10-2
Critical Resource Diagramming (CRD), 10-2
Cross product, 11-12. See also Vectors
C/SCSC. See Cost/schedule control systems
criteria (C/SCSC)
Cube, 2-32
Cubit, B-2
CumSlip chart. See Cumulative slippage
(CumSlip) chart
Cumulative failure rate, 9-10, 9-11
Cumulative slippage (CumSlip) chart,
10-12–13, 10-15. See also Gantt
charts
Cumulative sum chart (CUSUM), 3-25,
4-16, 8-4
Curve fitting. See Regression analysis
CUSUM. See Cumulative sum chart (CUSUM)
Cutting tools, 6-10
horsepower, 6-11–12
notations, 6-10–11
pressure, 6-11
pressure calculation, 6-11
Cycle time, 6-18
Cyclic-inscriptable quadrilateral, 2-30–2-31
Cyclic quadrilateral, 2-29
Cylinder, right circular, 2-34, 11-23
D
Data analysis and probability, 1-15
Data collection, 8-5
sampling frequency, 8-6
subgroup sample size, 8-5–6
DB method. See Declining Balance
(DB) method
Decibel, B-2
Decision(s), 9-1
actions, 9-3
consequences, 9-3
CPM, 9-2–3
events, 9-3
PERT, 9-3
probability summary, 9-7, 9-8
probability tree diagram, 9-5
problem, 9-2–4
tables and trees, 9-2
task selection, 9-3, 9-4
tree analysis, 9-2
Declining Balance (DB) method, 5-16–17
De Morgan’s laws, 2-9–10
Density function
failure, 9-9, 9-10, 9-11
probability, 2-4
triangular probability, 10-19, 10-20
uniform probability, 10-19, 10-20
Derivative, 11-16, 11-18–19. See also
Differential calculus
Descendent activity, 10-4
Descriptive statistics
average, 4-1
categorical analysis, 4-18–22
estimation, 4-4–5
normal probability plot, 4-5
Poisson rates comparison, 4-5
regression, 4-12–13
smoothness, 8-11
standard deviation, 4-2–3
standard error of mean, 4-3–4
statistical quality control, 4-13–16
time-series analysis, 4-16–18
variance, 4-1
Determinants, 11-12
Determination coefficient, 7-5–6
Difference equations, 11-24
first-order linear, 11-25
second-order linear, 11-25
Differencing, 7-10
Differential calculus, 11-16
curvature in rectangular coordinates,
11-17
derivative, 11-16
partial derivative, 11-16–17
radius of curvature, 11-17
test for maximum, 11-16
test for minimum, 11-16
test for point of inflection, 11-16
Discount option
cost curves, 7-17
evaluation, 7-17
optimal order quantity, 7-18
Discrete uniform distribution. See
Rectangular—distribution
Discrete Weibull distribution, 3-3, 3-32
Displacement, 12-3, 12-6. See also
Distance
angular, 12-3
Distance, 12-3, 12-4, 12-5, 12-7, 12-8, 12-9
conversion factors, C-5
point to line, from, 2-38
point to plane, from, 2-44
two points, between, 2-37, 2-43Index-6 Index
Distributions
Arcsin, 3-4, 3-34
Bernoulli, 3-1, 3-32
beta, 3-5, 3-35
beta binomial, 3-1, 3-32
beta Pascal, 3-3, 3-32
binomial, 3-3, 3-32
Cauchy, 3-5, 3-35
Chi, 3-5, 3-35
Chi-square, 3-5, 3-35
continuous formulas, 3-4, 3-34
discrete formulas, 3-1, 3-32
discrete Weibull, 3-3, 3-32
Erlang, 3-5, 3-35
exponential, 3-6, 3-35
extreme-value, 3-6, 3-36
F, 3-6, 3-36
gamma, 3-7, 3-36
geometric, 3-3, 3-33
half-normal, 3-7, 3-36
hypergeometric, 3-3–4, 3-33
Laplace, 3-7, 3-37
logistic, 3-7, 3-37
lognormal, 3-7, 3-37
negative binomial, 3-4, 3-33
noncentral Chi-square, 3-8, 3-37
noncentral F, 3-8, 3-38
noncentral t-distribution, 3-8, 3-38
normal, 3-9, 3-38
parameters, 3-10–11
Pareto, 3-9, 3-38
Poisson, 3-4, 3-34
probability, 2-3
Rayleigh, 3-9, 3-39
rectangular, 3-4, 3-34
t-distribution, 3-9, 3-39
triangular, 3-10, 3-39
uniform, 3-10, 3-39
Weibull, 3-10, 3-40
Distributive law, 2-9, 2-17
Dot product, 11-12. See also Cross product
Double exponential distribution.
See Laplace—distribution
Drill
horsepower, 6-14
thrust, 6-13–14
torque, 6-14
Dummy, 10-4
Durand’s rule, 2-31
Dynamics, 12-10
conservation of momentum law, 12-11
friction, 12-11
impulse of force, 12-11
momentum of force, 12-10
Newton’s laws of motion, 12-10
E
Earliest completion (EC) time, 10-5
Earliest starting (ES) time, 10-4, 10-11
EC. See Earliest completion (EC) time
Economic analysis, 1-15, 5-26
after-tax, 5-21–22
annuities, 5-4–5
compound interest, 5-2–4
equity break-even point, 5-8–10
equity computations, 5-5–8
future value, 5-1–2
loans amortization, 5-5
periodic payment, 5-5
simple interest, 5-1
Economic methods
annual value analysis, 5-10–11
external rate of return analysis, 5-11
incremental analysis, 5-11–12
incremental cash-flow approach, 5-12
internal rate of return analysis, 5-11
present value analysis, 5-10
total cash-flow approach, 5-12
Economic order quantity (EOQ) model, 7-15
basic inventory pattern, 7-15
costs as replenishment quantity functions,
7-16
TRC, 7-15
Effectiveness equation, 1-3
Electrical circuit equation, 7-4–5
Electronic Numerical Integrator and
Computer (ENIAC), 1-13
Elementary functions, A-3
Ellipse, 2-41, 11-3, 11-4, 11-21
area, 2-31
conic section, 11-4, 11-6
perimeter, 2-31
Ellipsoid, 2-36, 2-42
Employee group, 8-3
Energy, 12-13. See also Work
conservation, 12-14
conversion factors, C-2
English and metric systems, C-7
ENIAC. See Electronic Numerical Integrator
and Computer (ENIAC)Index Index-7
EOQ model. See Economic order
quantity (EOQ) model
Equity break-even point, 5-8
benefitcost ratio, 5-9
discounted payback period, 5-10
internal rate of return, 5-9
payback period, 5-9
sinking fund payment, 5-9
Ergonomics, 1-15
Erlang distribution, 3-5, 3-35, 4-6
ES time. See Earliest starting (ES) time
Eta, 3-29, 4-20–21
Euler’s identity, 11-11
Euler’s rule. See Forward rectangular rule
EWMA. See Exponentially weighted
moving average (EWMA)
Excise tax, 5-22
Executive leadership, 8-3
Exponential
distribution, 3-6, 3-35, 4-7, 9-9
function, 2-49, 2-50
Exponentially weighted moving average
(EWMA), 8-4
Extreme-value distribution, 3-6, 3-36
F
Facility design, 1-15
Factor, C-1. See also Conversion factor
Failure rate, 9-9, 9-10, 9-11
FCFS. See First Come, First Served (FCFS)
F distribution, 3-6, 3-14, 3-36, 4-7
Fibonacci number sequence, 11-25
FIFO. See First-in, first-out basis (FIFO)
First Come, First Served (FCFS), 1-19
First cost, 5-13, 5-24. See also Total cost
challenger, 5-13
defender, 5-13
recovery rate, 5-16
First-in, first-out basis (FIFO), 1-17
Flow balance equations, 1-21
Flow equation conservation. See Flow balance
equations
Forecasting, 7-1
based on averages, 7-1
exponential smoothing forecast, 7-3
extrinsic, 7-1
intrinsic, 7-1
inventory control, 7-15
period moving average forecast, 7-2
simple average forecast, 7-1
types, 7-1
weighted average forecast, 7-2
weighted T-period moving average
forecast, 7-2–3
Foreign exchange rates, 5-21
Forward-pass calculations, 10-5, 10-7
Forward rectangular rule, 11-26. See also
Numerical integration algorithms
Free-falling object, 12-7
Free slack (FS), 10-8
Freidman test, 3-18–19, 4-11
Freight ton, B-2
Frequency, 12-3
sampling, 8-6
Friction, 12-11
Frustum, 2-33
FS. See Free slack (FS)
Fulcrum, 12-1
G
Gamma distribution, 3-7, 3-36, 4-7
Gantt charts, 1-9, 10-10
based on ESs, 10-11
based on LSs, 10-12
fully crashed CPM network, 10-17
linked bars in, 10-13
milestone, 10-14
multiple-project, 10-15
phase-based, 10-14
progress monitoring, 10-13
task combination, 10-14
GD. See General queue discipline (GD)
GDS. See General Depreciation System (GDS)
General Depreciation System (GDS), 5-17
General queue discipline (GD), 1-17
Geometric distribution, 3-3, 3-33, 4-6
Geometric progression (G.P.), 2-15, 11-14–15
Geometry
Ceva’s Theorem, 2-27
circular cylinder, 2-35
lune, 2-36
Menelaus’ Theorem, 2-27
planar areas, 2-31
Prolemy’s theorem, 2-29
quadrilaterals, 2-27–31
right circular cone, 2-35
right circular cylinder, 2-34–35
solids bounded by planes, 2-31–33
sphere, 2-34
spherical polygon, 2-36Index-8 Index
Geometry (Continued)
spherical sector, 2-36
spheroids, 2-36–37
triangles, 2-25–27
Goal dimension calculation, 6-12–13
G.P. See Geometric progression (G.P.)
Gravitational force, 12-12
Gravity, 12-11
centrifugal force, 12-12
centripetal force, 12-12
conservation of energy, 12-14
energy, 12-13
gravitational force, 12-12
laws, 12-11
power, 12-14
torque, 12-12
work, 12-13
Greek alphabets, 2-16–17, E-1
Green belt, 8-3
Gross, B-2
H
Half-normal distribution, 3-7, 3-36
Harmonic mean, 2-20
cubic equations solution, 2-21–22
generalized mean, 2-20–21
quadratic equations solution, 2-21
Hartley’s test, 3-18, 4-10
Hertz, B-2
Hogshead, B-2
Hölder mean. See Harmonic
mean—generalized mean
Horizontal Projection, 12-8
Horsepower, 6-11–12, B-2
Household measurement conversion, C-7
Hyperbola, 11-4
Hypergeometric distribution, 3-3–4, 3-33
I
IE. See Industrial engineering (IE)
IF. See Independent float (IF)
Improvement goal
unit time, in, 6-6
Improvement ratio, 6-5
Impulse of force, 12-11
Inclined plane, 12-2
MA, 12-2
rolling motion, 12-9–10
sliding motion, 12-8–9
Income tax, 5-21
Indefinite integrals, 11-20–21
Independent float (IF), 10-8
Industrial engineer, 1-5, 8-9, 8-12
functions, 11-1
Industrial engineering (IE), 1-1–2, 1-4, 3-1
activities, 1-6
agricultural industry innovation, 1-8
analytical approach, 1-2
applications, 1-2, 1-5
Bridge proposals, 1-4
calculations guide importance, 1-16
catchphrases, 1-6
chronological events, 1-10–14
decision problem solving, 1-3
diverse areas, 1-15
effectiveness equation, 1-3
Einstein’s quote, 1-3, 1-4
forerunners, 1-8
functions, 1-5
historical accounts, 1-8–9
industrial engineer, 1-5
mass production techniques, 1-8
mathematical formulation
pseudo-code, 1-2
operational properties use, 1-2
orientation to STEM, 1-6
queuing system, 1-17–21
subareas, 1-7
sustainability, 1-2
versatility, 1-4
Industry, 1-7, 1-15. See also Industrial
engineering (IE)
agricultural innovation, 1-8
occupational discipline, 1-7
society infrastructures, 1-7
success of six sigma, 8-2
Inequalities, 2-47
Inertia, law of, 12-10. See also Newton’s laws of
motion
Inflation, 5-36, 5-38–39
causes, 5-36, 5-37
classic concepts, 5-39
combined interest rate, 5-37
commodity escalation rate, 5-37, 5-38
“constant worth” cash flow, 5-37, 5-38
effects, 5-37
hyper, 5-40
“market basket” rate, 5-37
mild, 5-40
moderate, 5-40Index Index-9
severe, 5-40
“then-current” cash flow, 5-37, 5-38
Integral calculus, 11-18
definite integral, 11-18
derivatives, 11-18–19
indefinite integrals, 11-20–21
integration methods, 11-18
Interest and equity computations, 5-5–7
Interest factor, D-1
formulas, D-1–2
Interest tables, D-3
0.25%, D-3–4
0.5%, D-5–6
0.75%, D-6–7
1%, D-7–8
10%, D-23
12%, D-24
1.25%, D-8–9
14%, D-25
1.5%, D-10
16%, D-26
1.75%, D-11
18%, D-27
2%, D-12
20%, D-28
2.5%, D-13
25%, D-29
3%, D-14
30%, D-30
3.5%, D-15
4%, D-16
4.5%, D-17
5%, D-18
6%, D-19
7%, D-20
8%, D-21
9%, D-22
Interfering slack (IS), 10-8
Internal rate of return (IRR), 5-9, 5-11, 5-26,
5-32–33
Interval scale, 1-22
IRR. See Internal rate of return (IRR)
IS. See Interfering slack (IS)
K
Kaizen, 8-23
Karat, B-2
Kendall’s Tau b, 3-30
measure, 4-21
Kinematics, 12-3
scalars and vectors, 12-3
uniform accelerated linear motion, 12-4
uniform accelerated rotation, 12-5
uniform rotation and fixed axis, 12-5
Kinetic energy, 12-13. See also Potential energy
Knot, 2-59, B-1, B-2
Kolmogorov–Smirnov test, 3-16, 4-9
Kruskal–Wallis test, 3-18, 4-11
L
Lambda, 2-17, 3-28, 4-19
Laplace
distribution, 3-7, 3-37
transforms, 2-58
Laplacian, 2-16
of scalar function, 11-13
Last-in, first-out (LIFO), 1-17
Latest completion (LC) time, 10-5
Latest starting (LS) time, 10-5, 10-11
LC. See Latest completion (LC) time
League, B-2
Lean, 8-22
Kaizen of process, 8-23
principle, 8-23
process decomposition hierarchy, 8-23
production objective, 6-18–19
task rating matrix, 8-24
task value rating system, 8-24–25
Lean–Six-Sigma, 8-23
Learning curve
adjusting machine requirements, 6-9
analysis, 6-2
average cost model, 6-1
average unit time determination, 6-5
buffer production calculation, 6-8–9
computational example, 6-2–3, 6-5–6
exponent, 6-1, 6-2
forces required by cutting tools, 6-10–11
goal dimension calculation, 6-12–13
improvement goal in unit time, 6-6
improvement ratio, 6-5
learning factor calculation, 6-5
linear feed for material removal, 6-18
machine accuracy, 6-12
machine formula, 6-7–8
machine output capacities, 6-6
machines needed to meet output, 6-7
machines sequence output, 6-9–10
machine utilization ratio, 6-6
models, 6-1Index-10 Index
Learning curve (Continued)
productivity calculations, 6-5
speed and rotation calculation, 6-14
time rate for material removal, 6-17
time required to perform task, 6-5
total time calculation, 6-5
unit cost model, 6-4
volume of material removed, 6-17
Learning factor calculation, 6-5
Lever, 12-1, 12-14
fulcrum, 12-1
simple machines, law of, 12-1
L’ Hospital’s rule, 11-17
Life sciences, 1-15
LIFO. See Last-in, first-out (LIFO)
Light year, B-2
Limiting values, 2-47
Linear feed for material removal, 6-18
Line equation. See Straight line
equation
Line fitting. See Regression analysis
Log–Normal distribution, 3-15, 4-7
Logarithm(s), 2-15, 2-58, 11-6
exponential function, 2-49, 2-50
fundamental properties, 2-49
general base, to, 2-46
general powers definition, 2-49
identities, 2-46, 11-7
inequalities, 2-47
limiting values, 2-47
logarithmic curve, 2-42
periodic property, 2-50
polynomial approximations,
2-48, 2-50–2-52
series expansion, 2-47
slopes, 2-53
Logistic distribution, 3-7, 3-37
Log–linear model, 6-1. See also
Learning curve—models
Lognormal distribution, 3-7, 3-37
LS. See Latest starting (LS) time
Lune, 2-36
M
MA. See Mechanical advantage (MA)
Machine
accuracy, 6-12
formula alternate forms, 6-7–8
output capacities, 6-6
output computations, 6-9–10
required for specific output, 6-7
utilization ratio, 6-6
Machine requirements
adjustment, 6-9
calculation, 6-23
Maclaurin series, 11-16. See also Taylor’s series
expansion, 2-14
MACRS. See Modified accelerated cost
recovery system (MACRS)
Magnum, B-2
MA process. See Moving average (MA) process
Marginal cost, 5-14, 5-24, 6-3, 6-4
continuous product volume, 6-4
MARR. See Minimum attractive rate of return
(MARR)
Master belt, 8-3
Mathematical
calculations, 1-1
modeling, 1-1, 1-15
signs and symbols, 2-15–16
Matrices, 11-11
determinants, 11-12
identity matrix, 11-11
matrix addition, 11-11
matrix inverse, 11-12
matrix multiplication, 11-11
matrix transpose, 11-11
Mean time to failure (MTTF), 9-9, 9-10, 9-11
Measurement, 1-15
household measurement conversion, C-7
nominal, 6-12–13
performance, 9-2
units, 2-59–60, B-1
Mechanical advantage (MA), 12-1
inclined plane, 12-2
pulley, 12-2
screw, 12-2
wedge, 12-2
wheel-and-axle system, 12-1
Menelaus’ theorem, 2-27
Merge point, 10-4
Methods time measurement (MTM), 1-13
Minimum attractive rate of return
(MARR), 5-10, 5-22, 5-26
Modified accelerated cost recovery
system (MACRS), 5-16
annual book value, 5-18
annual depreciation amount, 5-18
combined interest rate, 5-19
commodity escalation rate, 5-19, 5-20, 5-21
depreciation, 5-20Index Index-11
GDS property classes, 5-19
inflation rate, 5-19
method, 5-17
property classes, 5-18
real interest rate, 5-18
requirements, 5-17
steps, 5-17
Moments of inertia, 11-24
Momentum, 12-10
law of momentum conservation, 12-11
Moving average (MA) process, 7-12
Moving range chart (MR chart), 8-4, 8-9
MR chart. See Moving range chart (MR chart)
MTM. See Methods time measurement (MTM)
MTTF. See Mean time to failure (MTTF)
Multiple correlation coefficient, 7-6
Multiple resources working together, 6-20
partial completion of work, 6-21
N
NAV. See Net annual value (NAV)
Negative binomial distribution, 3-4, 3-33, 4-6
Net annual value (NAV), 5-10–11
Net Present Value (NPV), 5-10
Newton’s algorithm, 11-25
Newton’s laws of motion, 12-10
Newton’s method
minimization, 11-25–26
root extraction, 11-25
NHPP. See Nonhomogeneous Poisson process
(NHPP)
Node, 10-3
Nominal scale, 1-22
Noncentral
Chi-square distribution, 3-8, 3-37
F distribution, 3-8, 3-38
t-distribution, 3-8, 3-38
Nonhomogeneous Poisson process
(NHPP), 125
Nonstock production (NSP), 1-14
Normal distribution, 2-6, 3-9, 3-38, 4-8
deviation spread, 4-3
half-normal distribution, 3-7, 3-36
log–normal distribution, 4-7
project duration, 10-21
Normal task duration, 10-15. See also
Crash task duration
normal cost, 10-16
NPV. See Net Present Value (NPV)
NSP. See Nonstock production (NSP)
Number sequence and patterns, A-1–3
Numbers and prefixes, B-3
Numerical integration algorithms, 11-26
O
Oblate spheroid, 2-36
Ohm, 2-60, B-1, B-2
Operations analysis, 1-15
Ordinal scale, 1-22
P
Parabola, 2-42
area, 11-21
conic section, 11-3
cubical, 2-41, 2-42
segment, 2-31
Parabolic rule, 2-31, 11-27. See also Numerical
integration algorithms
Paraboloid of Revolution, 11-23
Parallel axis theorem, 11-24. See also Moment
of Inertia
Parallelogram, 2-27, 11-22
Pareto distribution, 1-22, 3-9, 3-38, 8-25
Parsec, B-2
Partial derivative, 11-16–17. See also
Differential calculus
Partial fractions, 2-23
general terms, 2-24
higher degree factors, 2-25
non-repeated linear factors, 2-23
polynomial, 2-23
repeated linear factors, 2-24, 2-25
PCP. See Percentage cost penalty (PCP)
PDM. See Precedence Diagramming Method
(PDM)
PE. See Practice of engineering (PE)
Pearson’s R, 3-30, 4-21
Pendulum, 12-7
Percentage cost penalty (PCP), 7-20
Performance uncertainties, 9-2
Period, 12-3
compounding period, 5-2
payback period, 5-9
recovery, 5-16
PERT. See Program Evaluation and
Review Technique (PERT)
Physical science(s), 1-15
equations, 2-60, C-6
Pi (π), 2-17, B-2Index-12 Index
Pica, B-2
Pipe, B-2
Planar areas, 2-31
Plane analytic geometry
angle between two lines, 2-38
cardioid, 2-40
Cassinian curves, 2-41–42
catenary cosine, 2-40
circle, 2-40
coordinates transformation, 2-39
distance, 2-37, 2-38, 2-43–45
line equation, 2-37, 2-38
plane curves, 2-40
polar coordinates, 2-40
slope, 2-37
triangle area, 2-39
Plane curves, 2-40
Point, B-2
Point–slope form, 11-1. See also
Straight line equation
Poisson distribution, 2-5, 3-4, 3-34, 4-6
Polar coordinates, 2-40, 11-10–11
Polygon
regular, 2-28, 2-29, 11-23
spherical, 2-36
Polyhedron, regular, 2-33
Population mean, 2-6
Potential energy, 12-13
Power, 12-14
Power mean. See Harmonic
mean—generalized mean
Power series, 2-49, 11-15
Practice of engineering (PE), 1-16
Precedence Diagramming Method (PDM),
10-2
precedence diagram, 10-4
Predecessor activity, 10-4, 10-5
Pressure, 6-11
conversion factors, C-4
Prism, 2-32
Prismatoid, 2-33. See also Polyhedron,
regular
Prismoid, 11-23
Probability, 2-3
desired outcomes, 2-11
expected value, 2-12, 3-31
failure, 2-3
mean value, 2-12, 3-31
principles, 3-31
project completion time, 9-7
random sampling process, 2-11
random variable, 2-12, 3-31
terminology, 2-11, 3-30
Probability distribution, 2-3
cumulative plot, 2-4
density function on plot, 2-4
expected value, 2-4
failure, 2-3
mean standard error, 2-6, 2-7
t-distribution, 2-7
variance, 2-5
Probability tree diagram, 9-5. See also
Decision(s)
modified probability tree, 9-8
task selection, 9-5, 9-8
weather dependent task durations, 9-6
Process capability analysis, 8-20
Cp
and C
pk abuse, 8-22
capability index, 8-19–20, 8-21
capable process, 8-18
distribution, 8-18
inherent process variability, 8-21
Process variation
estimate, 8-8
unstable, 8-7
Production environment
machine requirements calculation, 6-23
personnel requirements calculation, 6-22
Profit ratio analysis, 5-42–43, 5-45
break-even chart, 5-45–46
computation, 5-44, 5-45
profit area versus loss area, 5-44
profit functions plot, 5-43
Program Evaluation and Review Technique
(PERT), 5-47, 9-3, 10-2
activity duration variance, 10-19
expected duration, 10-19
formulas, 10-19
network, 10-22
probability calculations, 10-22
project data, 10-22
skewed distribution, 10-24
symmetric distribution, 10-24
Progressions, 2-20, 11-14–15
arithmetic, 2-14
geometric, 2-15
Project analysis
activity precedence relationships, 10-4
activity time distributions, 10-19
control, 10-1
CPM scheduling, 10-2
Gantt charts plotting, 10-10Index Index-13
organizing, 10-1
PERT formulas, 10-19
planning, 10-1
project crashing, calculations for, 10-13
project duration, 10-18, 10-20
scheduling, 10-1
slacks calculation, 10-8
subcritical paths, calculations for, 10-9
Project cost estimation, 5-46
ballpark, 5-46
cost control limits, 5-48
cost variance estimation, 5-47
optimistic and pessimistic, 5-47
PERT formula, 5-47
Project crashing, 10-9
calculations for, 10-13
crashing options for CPM, 10-18
crashing ratios, 10-17
fully crashed CPM network, 10-16, 10-17
Project duration
analytical analysis, 10-20, 10-24
diagnostics, 10-18
normal distribution, 10-21
project deadline probability, 10-22–23
transformation formula, 10-21
Project scheduling. See Critical Path Method
(CPM)—scheduling
Prolate spheroid, 2-37
Prolemy’s theorem, 2-29
Property tax, 5-22
Pulley, 12-2
Pyramid, 2-32
frustum, 2-33
volume, 2-52
Q
QLF. See Quality loss function (QLF)
Quadratic equation, 2-1, 11-2, A-7
Chebyshev’s theorem, 2-2
combinations, 2-2, 2-3
exponents law, 2-57
overall mean, 2-2
permutation, 2-2
quadratic formula, 2-1, A-7–8
roots, 2-1, 2-57, A-7
solution, 2-21, 2-23, 2-57
Quadric surface, 11-6
Quadrilaterals
cyclic, 2-29
cyclic-inscriptable, 2-30–2-31
general, 2-28
parallelogram, 2-27
rectangle, 2-27
rhombus, 2-28
theorem, 2-28–2-29
trapezoid, 2-28
Quality control, 3-22
capability ratios, 3-23
C charts, 3-24
CUSUM chart, 3-25
multivariate control charts, 3-25
NP charts, 3-25
P charts, 3-24
R charts, 3-24
S charts, 3-24
statistical, 4-13
subgroup statistics, 3-22
U charts, 3-24
X bar charts, 3-22–23
Quality loss function (QLF), 8-1. See also
Taguchi loss function
Quantity discount, 7-16, 7-18–19
items subject to, 7-18
price breakpoint, 7-17
Queuing system, 1-17
arrival process, 1-17
birth–death processes, 1-21
calling population, 1-17
components, 1-17
limiting queue length, 1-20–21
mathematical models assumption, 1-22
notation and equations, 1-19
performance measures, 1-18
queue disciplines, 1-17–18
queuing formula, 1-20
service mechanism, 1-17
service time, 1-20
short-hand representation, 1-18–19
steady-state conditions, 1-18
Quintal, B-2
Quire, B-2
R
R. See Range (R)
Radius of curvature, 11-17
Range (R), 8-7
Range charts (R charts), 3-24, 4-15, 8-4
control limits based on, 8-7
Ratio scale, 1-23
Rayleigh distribution, 3-9, 3-39Index-14 Index
R charts. See Range charts (R charts)
Real interest rate, 5-37
Ream, B-2
Rectangular
distribution, 3-4, 3-34, 4-6
parallelepiped, 2-32
Regression
nonlinear, 3-21
notation, 3-19, 4-12
predictions, 3-20–21
ridge, 3-21–22
statistics, 3-19–20, 4-12–13
Regression analysis, 7-3. See also Residual
ANOVA, 7-3
control, for, 7-4–5
determination coefficient, 7-5–6
prediction, 7-4
procedure, 7-5
regression models, 7-4, 7-6
regression relationships, 7-3–4
residual analysis, 7-7
Reliability, 9-8, 9-10
calculations, 9-7
density function of failure, 9-9
exponential distribution, 9-9, 9-11
failure distribution function, 9-9
failure rate, 9-9
formulas, 9-7, 9-10
function, 9-8, 9-10
mean time to failure (MTTF), 9-9
system, 9-9, 9-10
Research, 1-15
Residual, 3-20, 4-12
ideal residual pattern, 7-7
interdependence of error terms, 7-8
nonconstant variance, 7-8
nonlinearity, 7-8
omission of independent variables, 7-9
presence of outliers, 7-9
regression model, 7-7
Restriction, 10-4
Return on investment (ROI), 5-26
Revolution, 12-4
Risk computations
cost uncertainties, 9-1
performance uncertainties, 9-2
probability summary, 9-7
schedule uncertainties, 9-2
uncertainty, 9-1
Roentgen, B-2
ROI. See Return on investment (ROI)
Rolling motion, 12-9–10
Roman numerals, E-2
Roots, 2-19, 11-11
cubic equation, 2-22
quadratic equation, 2-1, 2-57, A-7
Rotational
motion, 12-5
speed, 12-4
S
Sales tax, 5-22
Sample
correlogram, 7-14
point, 2-11, 3-30
Scalars, 12-3. See also Vectors
Scaling factor, 3-21, 10-10
Scatter plot, 3-12, 7-4
Schedule uncertainties, 9-2
Scheffe interval, 3-17, 4-10
Science and technology, 1-15
Science, technology, engineering, and
mathematics (STEM), 1-6
Scientific
constants, B-3
enquiry, 1-15
notation, B-1
Scientific thinking mechanism (STM), 1-13
Score, B-2
Screw, 12-2
Sensitivity analysis, 7-19
based on PCP, 7-20
Series expansion, 2-12, 2-47
arithmetic progression, 2-14
binomial theorem, 2-14
common functions, 2-12–14
exponential function, 2-49
geometric progression, 2-15
Maclaurin series expansion, 2-14
Sterling’s formula, 2-15
Taylor series expansion, 2-14
Series properties, 11-15
Service in random order (SIRO), 1-17
Set, 2-7–8
combinations, 2-11
counting elements, 2-10
De Morgan’s laws, 2-9–10
empty, 2-8
equality, 2-8
operations, 2-9
permutation, 2-10Index Index-15
subset, 2-8
terms and symbols, 2-8
union, 2-8
Venn diagrams, 2-8–9
Shaft Speed, 6-15
σ chart. See Standard deviation—chart
(σ chart)
Simple harmonic motion, 12-6
angled projections, 12-8
free falling object, 12-7
horizontal projection, 12-8
pendulum, 12-7
rolling motion, 12-9–10
sliding motion, 12-8–9
vertical project, 12-7
Simple machines, law of, 12-1
Simpson’s rule. See Parabolic rule
Sine formula. See Sine law
Sine law, 2-55, 2-56, 11-7
Sine rule. See Sine law
Single-minute exchange of dies (SMED), 1-14
SIRO. See Service in random order (SIRO)
Six Sigma, 8-1
benefits, 8-2
champion, 8-3
control charts, 8-4, 8-8
control limits calculation, 8-7–8
data collection strategies, 8-5
out-of-control patterns, 8-6
process capability analysis, 8-18
project sponsor, 8-3
project team members, 8-3
roles and responsibilities, 8-3
SPC, 8-3–4
stable process, 8-6
X and R-charts, 8-4
Slacks calculation, 10-8
Sliding motion, 12-8–9
SL method. See Straight-Line (SL) method
Slope, 2-37, 2-53, 11-1
Slope–intercept form, 11-1. See also
Straight line equation
SMED. See Single-minute exchange
of dies (SMED)
Social sciences, 1-6, 1-15
Solids bounded by planes, 2-31
cube, 2-32
frustum, 2-33
prism, 2-32
prismatoid, 2-33
prismoidal formula, 2-33
pyramid, 2-32–33
rectangular parallelepiped, 2-32
regular polyhedra, 2-33
truncated triangular prism, 2-32
Somer’s D, 3-29, 4-20
Span, B-2
SPC. See Statistical process control (SPC)
Speed, 12-3, 12-4
free-falling object, 12-7
of light, B-3
vertical project, 12-7
Speed and rotation, 6-14
shaft speed, 6-15
surface speed, 6-15–16
tool feed per minute, 6-16
tool feed per revolution, 6-16
tool feed per tooth, 6-17
Sphere, 2-34, 2-42, 11-22. See Quadric surface
equation, 2-45
Spherical sector, 2-36
Spheroids
circular torus, 2-37
ellipsoid, 2-36
oblate spheroid, 2-36
prolate spheroid, 2-37
Square, B-3
Stable process, 8-6. See also Unstable process
Standard deviation, 3-11, 4-7, 7-10, 9-7, 9-10
application areas, 4-2
chart (σ chart), 8-4
normal distribution deviation spread, 4-3
sample, 4-2
subgroup, 3-22, 4-13
Standard error of mean, 4-3. See also Standard
deviation
application areas, 4-3
kurtosis, 4-4
response, 3-21, 4-13
skewness, 4-3
standardized kurtosis, 4-4
standardized skewness, 4-3
weighted average, 4-4
Statistical distributions, 3-2
normal probability plot, 3-12
parameter estimation, 3-11–12, 3-13–16
parameters, 3-10–12
Poisson rates comparison, 3-13
Statistical process control (SPC), 8-3
Statistical quality control
capability ratios, 4-14
C charts, 4-15Index-16 Index
Statistical quality control (Continued)
CUSUM chart, 4-16
NP charts, 4-15
P charts, 4-15
R charts, 4-15
S charts, 4-15
subgroup statistics, 4-13
U charts, 4-15
X-bar charts, 4-14
STEM. See Science, technology, engineering,
and mathematics (STEM)
Sterling’s formula, 2-15
STM. See Scientific thinking
mechanism (STM)
Stone, B-3
Straight line equation, 2-37, 2-38, 2-53, 6-2
angle between lines, 11-1
distance between two points, 11-2
general form, 11-1
point–slope form, 11-1
slope, 11-1
slope–intercept form, 11-1
standard form, 11-1
Straight-Line (SL) method, 5-16
Student’s t-distribution. See t-distribution
Subcritical paths, 10-9
analysis, 10-11
criticality level, 10-10
identification, 10-10
Successor activity, 10-4
Sums-of-Years’ Digits (SYD) method, 5-17
Surface Speed, 6-15–16
Survival function. See Reliability—function
SYD method. See Sums-of-Years’ Digits (SYD)
method
System reliability, 9-9, 9-11
T
t. See Activity duration (t)
Taguchi loss function, 8-1
actual cost, 8-2
actual loss, 8-2
defects sources, 8-2
opportunity cost, 8-1
productivity loss, 8-2
QLF, 8-1
six sigma, 8-3
time lost, 8-1, 8-2
waste, 8-2
Takt time, 6-18. See also Lean
limitation, 6-19
production crew size, 6-19
Tangent
curve, 2-42
inverse tangent curve, 2-42
length, 11-5
tangential acceleration, 12-5
Tau C, 3-30, 4-22
Taylor, Frederick Winslow, 1-8–9. See also
Taylor’s series
Taylor’s series, 11-16
expansion, 2-14
t-distribution, 2-7, 3-9, 3-39. See also
Probability distribution
Therm, B-3
Time rate for material removal, 6-17
Time required
to double investment, 5-35
to perform task, 6-5. See Normal task
duration
Time-series analysis, 7-9, 7-14
autocorrelation, 3-26, 4-17
autoregressive processes, 7-13
box-cox, 3-26, 4-17
cross-correlation, 3-26, 4-17
discount option evaluation, 7-17
economic order quantity model, 7-15
forecasting for inventory control, 7-15
moving average processes, 7-12
notation, 3-25, 4-16
partial autocorrelation, 3-26, 4-17
periodogram, 3-27, 4-18
principle, 7-9
quantity discount, 7-16
sensitivity analysis, 7-19
stationarity and data
transformation, 7-10
total relevant cost calculation, 7-16
Wagner–Whitin algorithm, 7-20
TMC. See Total marginal cost (TMC)
Tool feed
per minute, 6-16
per revolution, 6-16
per tooth, 6-17
Torque, 12-12
drill, 6-14
Total cost, 6-4, 5-25
continuous product volume, 6-4
operation, 5-40
Total marginal cost (TMC), 5-15
Total relevant cost (TRC), 7-15, 7-16Index Index-17
Total slack (TS), 10-8
for activity F, 10-9
minimum, 10-9
Total time for job, 6-5
Township, B-3
Transformation formula, 10-21
Transforms
functional products, 2-59
Laplace, 2-58
operational properties, 2-58
Trapezoidal rule, 2-31, 11-26. See also
Numerical integration algorithms
TRC. See Total relevant cost (TRC)
Triangles, 2-25
area, 2-39, 5-43
Ceva’s theorem, 2-27
equilateral, 2-26
general, 2-26–27
Menelaus’ theorem, 2-27
right, 2-26
right triangle calculations, 2-55
spherical, 2-36
for trigonometric functions, 11-8
Triangular
distribution, 3-10, 3-39, 4-8
probability density function, 10-19, 10-20
Trigonometry
angle relationships, 2-55
complex numbers, 11-10
cubic equation, 2-22
identities, 11-8–10
law of cosines, 11-8
law of sines, 11-7
right triangle calculations, 2-54–55
triangle equations, 2-54
triangles for, 11-8
trigonometric functions, 11-7
trigonometric ratios, 2-53
Trig ratio values, 2-60
Truncated triangular prism, 2-32
TS. See Total slack (TS)
Tukey interval, 3-17, 4-10
Tun, B-3
U
Uncertainty, 9-1
coefficient, 3-28, 4-19
Uniform
distribution, 3-10, 3-39, 4-8
linear motion, 12-4
probability density function, 10-21. See also
Beta distribution
rotation and fixed axis, 12-5
Uniform accelerated
linear motion, 12-4
rotation, 12-5–6
Unit cost model, 6-4
Unstable process, 8-6
average, 8-7
average and variation, 8-8
variation, 8-7
V
VA. See Value analysis (VA)
Value analysis (VA), 1-13
annual, 5-10–11
present, 5-10
Variance, 2-5, 2-6, 3-11, 9-7, 9-10. See also
Standard deviation
application areas, 4-1–2
calculations, 4-2
equal, 3-12, 4-4
sample, 4-1
sample estimates, 7-12
theoretical, 7-11
unequal, 3-12, 4-4
Variate generation techniques, 3-42
accelerated life model, 3-40
algorithms, 3-40–41
formulas, 3-41
proportional hazards model, 3-40
Vectors, 11-12, 12-3
gradient, divergence, and curl,
11-13
identities, 11-13–14
Laplacian of scalar function,
11-13
Velocity, 12-3. See also Speed
angled projections, 12-8
conversion factors, C-4
rolling motion on inclined plane,
12-9
rotational motion, 12-5
simple harmonic motion, 12-6
sliding motion on inclined plane,
12-8, 12-9
trajectory, 12-8
Vertical project, 12-7
Volume of material removed, 6-17Index-18 Index
W
Wagner–Whitin (W–W) algorithm, 7-20
optimality properties, 7-21
propositions, 7-21–22
total inventory cost, 7-21
Watt, 2-60, 12-14, B-1, B-3
Weddle’s rule, 2-31
Wedge, 12-2. See also Inclined plane
Weibull distribution, 3-10, 3-16, 3-40, 4-8
discrete, 3-3, 3-32
WF. See Work factors (WF)
Wheel and axle, 12-1
WIP. See Work-in-process (WIP)
Work, 6-19, 12-13
Work factors (WF), 1-13
Work-in-process (WIP), 5-23
Work rate analysis, 6-19
construction, 6-21
Work rate table, 6-20
alternate work, 6-22
incorporation of cost, 6-22
multiple resource units, 6-21
single resource unit, 6-20
W–W algorithm. See Wagner–Whitin (W–W)
algorithm
Z
Zero project slack convention, 10-5. See also
Forward-pass calculations


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