Handbook of Industrial Engineering Equations, Formulas, and Calculations

Cover......Page 1
Mini Title......Page 2
Series Publications......Page 3
Title......Page 5
Copyright......Page 6
Dedications......Page 7
Contents......Page 8
Preface......Page 28
Authors......Page 30
Industrial Engineering and Computations......Page 32
Definition and Applications......Page 36
Span and Utility of IE......Page 37
Heritage from Industrial Revolution......Page 38
Historical Accounts......Page 39
Chronology of Applications......Page 41
Importance of IE Calculations......Page 45
Importance of Calculations Guide......Page 47
Basic Queuing Equations......Page 48
Queuing Birth–Death Law 3......Page 52
Interval Scale......Page 53
References......Page 54
Quadratic Equation......Page 55
Combinations......Page 56
Distribution Function......Page 57
Expected Value......Page 58
Poisson Distribution......Page 59
Standard Error of the Mean......Page 60
Definition of Set and Notation......Page 61
Venn Diagrams......Page 62
De Morgan\'s Laws......Page 63
Permutations......Page 64
Basic Probability Principles......Page 65
Series Expansions......Page 66
Mathematical Signs and Symbols......Page 69
Greek Alphabets......Page 70
Special Products and Factors......Page 71
Proportion......Page 73
Generalized Mean......Page 74
Solution of Cubic Equations......Page 75
Trigonometric Solution of the Cubic Equation......Page 76
Nonrepeated Linear Factors......Page 77
General terms......Page 78
Triangles......Page 79
General Triangle......Page 80
Parallelogram......Page 81
Circle of radius r......Page 82
Prolemy\'s Theorem......Page 83
Segment of a Circle of Radius r......Page 84
Solids Bounded By Planes......Page 85
Pyramid......Page 86
Regular Polyhedra......Page 87
Right Circular Cylinder of Radius r and Height h......Page 88
Zone and Segment of Two Bases......Page 89
Oblate Spheroid......Page 90
Equation of a Line Joining Two Points......Page 91
Angle ψ between Two Lines Having Slopes m1 and m2......Page 92
Transformation of Coordinates Involving Translation and Rotation......Page 93
Circle......Page 94
Cassinian Curves......Page 95
Logarithmic Identities......Page 100
Inequalities......Page 101
Polynomial Approximations......Page 102
Definition of General Powers......Page 103
Periodic Property......Page 104
Trigonometric ratios......Page 107
Sine Law......Page 109
Expanding......Page 110
Law of exponents......Page 111
Roots of a Quadratic Equation......Page 0
Logarithms......Page 112
Beta Binomial Distribution......Page 115
Hypergeometric Distribution......Page 117
Arcsin Distribution......Page 118
Erlang Distribution......Page 119
F Distribution......Page 120
Lognormal Distribution......Page 121
Noncentral t-Distribution......Page 122
t-Distribution......Page 123
Distribution Parameters......Page 124
Estimation and Testing......Page 125
Normal Probability Plot......Page 126
Poisson......Page 127
Gamma......Page 128
Uniform......Page 129
Notation......Page 130
Cochran C-Test......Page 131
Freidman Test......Page 132
Regression Statistics......Page 133
Predictions......Page 134
Ridge Regression......Page 135
X Bar Charts......Page 136
Capability Ratios......Page 137
P Charts......Page 138
Time-Series Analysis......Page 139
Box-Cox......Page 140
Chi-Square......Page 141
Uncertainty Coefficient......Page 142
Eta......Page 143
Probability Terminology......Page 144
Mean Value x or Expected Value μ......Page 145
Discrete Weibull Distribution......Page 146
Negative Binomial Distribution......Page 147
Arcsin Distribution......Page 148
Exponential Distribution......Page 149
Half-Normal Distribution......Page 150
Noncentral Chi-Square Distribution......Page 151
Pareto Distribution......Page 152
Uniform Distribution......Page 153
Variate Generation Algorithms......Page 154
References......Page 156
Application Areas......Page 157
Application Areas......Page 158
Standardized Skewness......Page 159
100(1 – α)% Confidence Interval for Difference in Means......Page 160
Binomial Distribution......Page 161
Erlang Distribution......Page 162
Log–Normal Distribution......Page 163
Chi-Square Test for Distribution Fitting......Page 164
Interval Estimates......Page 165
Hartley\'s Test......Page 166
Freidman Test......Page 167
Notation......Page 168
Subgroup Statistics......Page 169
Capability Ratios......Page 170
P Charts......Page 171
Notation......Page 172
Box-Cox Computation......Page 173
Chi-Square......Page 174
Uncertainty Coefficient......Page 175
Eta......Page 176
Pearson\'s R Measure......Page 177
Failure......Page 178
Simple Interest......Page 179
Compound Interest......Page 180
Annuities......Page 182
Interest and Equity Computations......Page 183
Equity Break-Even Formula......Page 186
Sinking Fund Payment......Page 187
Annual Value Analysis......Page 188
Incremental Analysis......Page 189
Asset Replacement and Retention Analysis......Page 190
Replacement Analysis Computation......Page 192
Depreciation Terminology......Page 193
Declining Balance (DB) Method......Page 194
MACRS Method......Page 195
Effects of Inflation and Taxes......Page 196
After-Tax Economic Analysis......Page 199
Cost and Value Computations......Page 200
Estimated Cost at Completion......Page 201
Operating Cost......Page 202
Variable cost......Page 203
Calculations with Compound Amount Factor......Page 204
Calculations with Uniform Series Present Worth Factor......Page 205
Calculations with Uniform Series Capital Recovery Factor......Page 206
Calculations with Uniform Series Compound Amount Factor......Page 207
Calculations with Capitalized Cost Formula......Page 208
Arithmetic Gradient Series......Page 209
Internal Rate of Return......Page 210
Simple Payback Period......Page 211
Discounted Payback Period......Page 212
Time Required to Double Investment......Page 213
Effects of Inflation on Industrial Project Costing......Page 214
Break-Even Analysis......Page 218
Profit Ratio Analysis......Page 220
Project Cost Estimation......Page 224
Cost Performance Index......Page 225
Project Balance Computation......Page 226
The Average Cost Model......Page 227
Computational Example......Page 228
Computational Example......Page 229
The Unit Cost Model......Page 230
Computational Example......Page 231
Computation of Machine Output Capacities......Page 232
Calculating Number of Machines Needed to Meet Output......Page 233
Calculating Buffer Production to Allow for Defects......Page 234
Calculating Forces on Cutting Tools......Page 236
Calculating the Goal Dimension......Page 238
Calculating Speed and Rotation of Machines......Page 240
Computation to Find the Volume of Material Removed......Page 243
Takt Time for Production Planning......Page 244
Production Crew Work Rate Analysis......Page 245
Case of Multiple Resources Working Together......Page 246
Computational Examples......Page 247
Calculation of Personnel Requirements......Page 248
References......Page 249
Simple Average Forecast......Page 250
Weighted T-Period Moving Average Forecast......Page 251
Regression Relationships......Page 252
Control......Page 253
Coefficient of Determination......Page 254
Residual Analysis......Page 256
Time-Series Analysis......Page 258
Stationarity and Data Transformation......Page 259
Moving Average Processes......Page 261
Autoregressive Processes......Page 262
Economic Order Quantity Model......Page 264
Calculation of Total Relevant Cost......Page 265
Evaluation of the Discount Option......Page 266
Sensitivity Analysis......Page 268
Wagner–Whitin Algorithm......Page 269
Notation and Variables......Page 270
Taguchi Loss Function......Page 272
Identification and Elimination of Sources of Defects......Page 273
Statistical Techniques for Six Sigma......Page 274
X and R-Charts......Page 275
Data Collection Strategies......Page 276
Out-of-Control Patterns......Page 277
Calculation of Control Limits......Page 278
Plotting Control Charts for Range and Average Charts......Page 279
Calculations......Page 280
Trend Analysis......Page 285
Capable Process (Cp)......Page 289
Capability Index (Cpk )......Page 290
Process Capability Example......Page 291
Possible Applications of Process Capability Index......Page 292
Lean Principles and Applications......Page 293
Kaizen of a Process......Page 294
Lean Task Value Rating System......Page 295
Cost Uncertainties......Page 297
Decision Tables and Trees......Page 298
Reliability Calculations......Page 303
General Reliability Definitions......Page 304
Exponential Distribution Used as Reliability Function......Page 305
General Reliability Definitions......Page 306
Exponential Distribution Used as Reliability Function......Page 307
Scheduling......Page 308
CPM Scheduling......Page 309
Advantages for Team Interaction......Page 310
Network Notation......Page 311
Forward-Pass Calculations......Page 312
CPM Example......Page 313
Backward-Pass Calculations......Page 314
Calculation of Slacks......Page 315
Calculations for Subcritical Paths......Page 316
Plotting of Gantt Charts......Page 317
Calculations for Project Crashing......Page 320
Calculations for Project Duration Diagnostics......Page 325
Activity Time Distributions......Page 326
Project Duration Analysis......Page 327
Simulation of Project Networks......Page 331
Equation of a Straight Line......Page 333
Conic Sections......Page 334
Case 2 of Conic Section: e < 1 (Ellipse)......Page 335
Case 3 Hyperbola: e > 1......Page 336
Case 4 e = 1 (Circle)......Page 337
Quadric Surface (Sphere)......Page 338
Law of Sines......Page 339
Identities......Page 340
Polar Coordinates......Page 342
Matrix Transpose......Page 343
Vectors......Page 344
Identities......Page 345
Geometric Progression......Page 346
Power Series......Page 347
The Derivative......Page 348
L\'Hospital\'s Rule......Page 349
Derivatives......Page 350
Indefinite Integrals......Page 352
Ellipse......Page 353
Parallelogram......Page 354
Paraboloid of Revolution......Page 355
Difference Equations......Page 356
Newton\'s Method of Minimization......Page 357
Numerical Integration......Page 358
Calculation of Best-Fit Circle......Page 359
Machine 2: Wheel and Axle......Page 362
Machine 6: The Screw......Page 363
Scalars and Vectors......Page 364
Uniform Accelerated Linear Motion......Page 365
Uniform Accelerated Rotation about a Fixed Axis......Page 366
Simple Harmonic Motion......Page 367
Vertical Project......Page 368
Sliding Motion on an Inclined Plane......Page 369
Rolling Motion on an Inclined Plane......Page 370
Momentum of Force......Page 371
General Law of Gravity......Page 372
Torque......Page 373
Energy......Page 374
Power......Page 375
Number Sequence and Patterns......Page 376
Closed-Form Mathematical Expressions......Page 378
Derivation of the Quadratic Formula......Page 382
Common Notation......Page 384
Numbers and Prefixes......Page 386
Area Conversion Factors......Page 387
Energy Conversion Factors......Page 388
Temperature Conversion Factors......Page 389
Pressure Conversion Factors......Page 390
Distance Conversion Factors......Page 391
Physical Science Equations......Page 392
Household Measurement Conversion......Page 393
Formulas for Interest Factor......Page 394
Interest Tables......Page 396
Greek Symbols......Page 424
Roman Numerals......Page 425
Bibliography......Page 426