Coating Substrates and Textiles: A Practical Guide to Coating and Laminating Technologies | Andreas Giessmann

Coating Substrates and Textiles: A Practical Guide to Coating and Laminating Technologies

by Andreas Giessmann

Contents

1 The Coating Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 1
1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Classification and Delineation of Coating . . . . . . . . . . . . . . . . 2
1.1.2 Textile Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Intelligent Textiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Historical Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Economic Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Demands of a Coating Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Logistic IntegrationWithin a Coating Facility . . . . . . . . . . . . . . . . . . . 12
2.1.1 Technical Performance/Services . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Logistic Performance/Services . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3 Sales Performance/Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Realisation of Logistical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Basic Elements of Coating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 The Roller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Application Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Knife Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Roller Application Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.3 Powder Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.4 Hot-Melt Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.5 Injecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.6 Slot Die and Pouring Technologies . . . . . . . . . . . . . . . . . . . . . . 47
3.2.7 Dipping and Impregnating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.8 Point and Double-Point Coating . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.9 Foam Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.10 Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3 Material Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.2 GuidingWeb Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.3 Material Reserves (Compensator) . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.4 Accumulator Trough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.5 Tenter Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.6 Drive Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 Auxiliary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 Drying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1 Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.2 Minimum Exhaust Volume Flow. . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.3 Temperature Control Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.4 Thermal Oil Boiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.5 Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Recording Data on Coating Systems for Quality Assurance
Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6.1 Recording Measured Values . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6.2 Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.3 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.4 Flow Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6.5 CoatingWeight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.6.6 Material Moisture Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Production Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1 Coating Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.1 Transfer Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.2 Direct Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Lacquering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Embossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Tumbling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.6 Combined Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7 Flock Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.8 Laminating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.8.1 Dry Laminating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.8.2 Wet Laminating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.8.3 Flame Laminating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.9 Final Assembly and Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.10 Reference Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5 Paste Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1 Vacuum Sinus Dissolver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Vacuum Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3 Three-Roller Mill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Wall-Mounted High-Speed Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.5 Solvent Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6 Plastisol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6.1 Preparations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6.2 Using a High Speed Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.6.3 Low Speed Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.6.4 De-Airing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.6.5 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6 Substrate Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.1 Properties of the End Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.1.1 Carrier Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.1.2 Coating of the Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.1.3 Coated Textiles as Laminate Materials . . . . . . . . . . . . . . . . . . . 108
6.2 Medical and Hygiene Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2.1 Product Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2.2 Substrates and Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.2.3 Process Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3 Prepreg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3.1 Product Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3.2 Substrates and Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.3.3 Process Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4 Thin Film Coating (In the Field of Electronics) . . . . . . . . . . . . . . . . . . 126
6.4.1 Substrate Pre-Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4.2 Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.4.3 Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4.4 Substrate Post-Treatment (and Subsequent Processes) . . . . . . 132
7 Characteristics and Applications of Plastisols and Additives . . . . . . . . . 135
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.1.2 PVC Resins for Plastisol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.1.3 What Is a Plastisol?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.2 Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.2.1 Viscosity According to Newton . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.2.2 Shear Stress τ =F/S is in dyn/cm . . . . . . . . . . . . . . . . . . . . . . . 138
7.2.3 Non-Newtonian Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.2.4 Rheologic Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.2.5 A Look at Actual Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.2.6 Thixotropy and Curing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.2.7 Elements in the Composition of a Plastisol . . . . . . . . . . . . . . . 140
7.2.8 PVC Resins for Plastisols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.3 The Plasticisers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.3.1 Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.3.2 What are Plasticisers Made of? . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.3.3 Their Performance Characteristics . . . . . . . . . . . . . . . . . . . . . . 145
7.3.4 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4 Stabilising Agents, Accelerators and Co-Stabilising Agents . . . . . . . . 152
7.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.4.2 Mercaptide Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.4.3 Carboxyl Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4.4 Barium/Zinc Stabilising Agents . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4.5 Calcium/Zinc Stabilising Agents . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4.6 Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.4.8 Co-stabilising Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.4.9 Epoxy Stabilising Agents or Plasticisers . . . . . . . . . . . . . . . . . 156
7.4.10 Epoxidised Soybean Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.4.11 Epoxidised Linseed Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.4.12 Octyl Epoxy Tallate and Isooctyl Epoxy Tallate . . . . . . . . . . . 157
7.5 Foaming or Expanding Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.5.1 Chemical Foaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.5.2 PVC Resin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.5.3 Plasticisers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.5.4 Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.5.5 Foaming Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.5.6 Azodicarbonamide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.5.7 Sulfonhydrazide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.5.8 Hydrocerole BIF (Böhringer Ingelheim) . . . . . . . . . . . . . . . . . 161
7.5.9 Practical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.5.10 Mechanical Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.5.11 Surface-active Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.5.12 Mixers for Mechanical Foams . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.5.13 Physical Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.6 Extenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.6.1 Carbonate Extenders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.6.2 Precipitated Calcium Carbonates . . . . . . . . . . . . . . . . . . . . . . . 167
7.6.3 Carbonate-free Extenders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.6.4 Additives with an Extender Function . . . . . . . . . . . . . . . . . . . . 168
7.6.5 General Influences of Extenders . . . . . . . . . . . . . . . . . . . . . . . . 169
7.7 Rheologic Modifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
7.7.1 The Thickening Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
7.7.2 Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.7.3 Substances for Flame Retardation and Smoke Suppression . . 173
7.8 UV Light Stabilising Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.8.1 Other Successes inWeather Resistance . . . . . . . . . . . . . . . . . . 182
7.8.2 Important UV Light Stabilisers . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.9 Adhesion Promoters for Plastisols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.9.1 Single-Component Adhesives . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.9.2 Two-Component Adhesives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.10 Biocides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.10.1 Microbiological Attack. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.10.2 Fungi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.10.3 Bacteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.10.4 Algae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.10.5 Common Biocides for Plastisol . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.11 Other Raw Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.11.1 Antistatic Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.11.2 Calcium Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.11.3 Air Releasing Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.12 Economy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.12.1 Relative Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.12.2 Formula Examples and Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8 Emission Control in Coating Companies . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.1 Air Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.1.1 Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.1.2 Immissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.1.3 Threshold Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.1.4 Air Quality Control Regulations . . . . . . . . . . . . . . . . . . . . . . . . 197
8.2 Emission Control Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.2.1 Procedure with Solid and Liquid Pollutants . . . . . . . . . . . . . . . 198
8.2.2 Procedure for Vaporous and Gaseous Pollutants . . . . . . . . . . . 202
8.2.3 Combination Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
8.3 Requirements for Emission Control Systems . . . . . . . . . . . . . . . . . . . . 211
8.4 Emission Control System Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
9 Investment Profitability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
9.1 Strategic Profitability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.2 The Business Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
9.3 Production Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
9.4 Coating Plant Cost Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
9.4.1 Investment Spending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
9.4.2 Operating Costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
9.4.3 Annuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
9.4.4 Total Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
9.5 Performance Elements in Coating Plants . . . . . . . . . . . . . . . . . . . . . . . 229
9.5.1 Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
9.5.2 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
9.5.3 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
9.6 Operational Profitability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
9.7 Planning Result Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
9.7.1 Annual Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
9.7.2 Profits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
9.7.3 Summary of All Costs and Profits . . . . . . . . . . . . . . . . . . . . . . . 235
9.7.4 Comparison Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . 237
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 241

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Composite Structures: Theory and Practice Edited by Peter Grant and Carl Q. Rousseau

Composite Structures: Theory and Practice

Edited by Peter Grant and Carl Q. Rousseau

Contents

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
STRUCTURAL DAMAGE TOLERANCE
USAF Experience in the Qualification of Composite Structures--J. w. LINCOLN . . . . . . . . 3
A Review of Some Key Developments in the Analysis of the Effects of Impact Upon
Composite Structures--R. OLSSON, L. E. ASP, S. NILSSON, AND A. SJOGREN . . . . . . . . . [2
Certificate Cost Reduction Using Compression-After-Impact Testing--T. C. ANDERSON . 29
SKIN-STRINGER BEHAVIOR
Mechanisms and Modeling of Delamination Growth and Failure of
Carbon-Fiber-Reinforced Skin-Stringer Panels--E. GREENHALGH, S. SINGH, AND
K. F. NILSSON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Parametric Study of Three-Stringer Panel Compression-After-lmpact
Strength--c. Q. ROUSSEAU, D. J. BAKER, AND J. DONN HETHCOCK . . . . . . . . . . . . . . . . . 72
A Method for Calculating Strain Energy Release Rates in Preliminary Design of
Composite Skin/Stringer Debonding Under Multiaxial Loading--R. KRUEGER,
P. J. MINGUET, AND T. K. O'BRIEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
ROTORCRAFT AND PROPELLER STRUCTURAL QUALIFICATION ISSUES
Fail-Safe Approach for the V-22 Composite Proprotor Yoke--L. K. ALTMAN, D. J. REDDY,
AND H. MOORE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
RAH-66 Comanche Building Block Structural Qualification Program--A. DOBYNS,
B. BARR, AND J. ADELMANN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
The Effects of Marcel Defects on Composite Structural Properties--A. CAIAZZO,
M. ORLET, H. McSHANE, L. STRAIT, AND C. RACHAU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Influence of Ply Waviness on Fatigue Life of Tapered Composite Flexbeam
Laminates--~. 8. MURRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Structural Qualification of Composite Propeller Blades Fabricated by the Resin
Transfer Molding Process--s. L. SMITH, AND J. L. MATTAVI . . . . . . . . . . . . . . . . . . . . 2 i0
BOLTED JOINT ANALYSIS
Three-Dimensional Stress Analysis and Failure Prediction in Filled Hole
Laminates--E. v. IARVE AND D. H. MOLLENHAUER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Damage-Tolerance-Based Design of Bolted Composite Joints--x. QING, H.-T. SUN,
L. DAGBA, AND F.-K. CHANG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Open Hole Compression Strength and Failure Characterization in Carbon/Epoxy
Tape Laminates--rE BAU, D. M. HOYT, AND C. Q. ROUSSEAU . . . . . . . . . . . . . . . . . . . . 273
The Influence of Fastener Clearance Upon the Failure of Compression-Loaded
Composite Bolted Joints----A. J. SAWlCKI and P. J. MINGUET . . . . . . . . . . . . . . . . . . . . . 293
Characterizing Delamination Growth in a 0~ ~ Interface--R. H. MARTIN AND
C. Q. ROUSSEAU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
New Experiments Suggest That All Shear and Some Tensile Failure Processes are
Inappropriate Subjects for ASTM Standards--M. R. PIGGOTT, K. LIU, AND
J. WANG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
Effect of Friction on the Perceived Mode II Delamination Toughness from Three- and
Four-Point Bend End-Notched Flexure Tests---c. SCHUECKER AND
B. D. DAVIDSON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
Finite-Element Analysis of Delamination Growth in a Multidirectional Composite ENF
Specimen--M. KONIG, R. KRUGER, AND S. RINDERKNECHT . . . . . . . . . . . . . . . . . . . . . . . 345
Comparison of Designs of CFRP-Sandwich T-Joints for Surface-Effect Ships Based on
Acoustic Emission Analysis from Load TestS--ANDREAS J. BRUNNER AND
ROLF PARADIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Development of a Test Method for Closed-Cross-Section Composite Laminates
Subjected to Compression Loading--R. B. BUCINELL AND B. ROY . . . . . . . . . . . . . . . 382
Tension Pull-off and Shear Test Methods to Characterize 3-D Textile Reinforced
Bonded Composite T e e - J o i n t s - - s . D. OWENS, R. e. SCHMIDT, AND J. J. DAVIS . . . . . . . 398
STRENGTH PREDICTION
What the Textbooks Won't Teach You About Interactive Composite Failure
C r i t e r i a - - L . J. HART-SMITH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Curved Laminated Beams Subjected to Shear Loads, Moments, and Temperature
Changes--s. o. PECK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
Damage, Stiffness Loss, and Failure in Composite S t r u c t u r e s - - s . N. CHAa~rE~EE . . . . . . . 452
Compressive Strength of Production Parts Without Compression
Testing--E. J. BARBERO AND E. A. WEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
ENVIRONMENTAL EFFECTS
Environmental Effects on Bonded Graphite/Bismaleimide Structural
Joints--K. A. LUBKE, L. M. BUTKUS, AND W. S. JOHNSON . . . . . . . . . . . . . . . . . . . . . . . . 493
Accelerated Tests of Environmental Degradation in Composite
Materials--T. G. REYNOLDS AND H. L. McMANUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
PLENARY SESSION
The Effects of Initial Imperfections on the Buckling of Composite Cylindrical
Shells--J. H. STARNES, JR., M. W. HILBURGER, and M. P. NEMETH . . . . . . . . . .. . . 529
Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 551

Overview
The Symposium on "'Composite Structures: Theory and Practice" sponsored by Committee D-30 on Composite Materials, was held in Seattle on 17th and 18th May 1999. This topic was a departure from the traditional D-30 symposia themes of "Design and Testing" and "Fatigue and Fracture." The reasons for this were to focus more specifically on structural certification/qualification issues, and to garner more interest and participation from government and industry experts. As stated in the Call for Papers, "'The objective of this symposium (was) to bring together practitioners and theoreticians in the composite structural mechanics field, to better understand the needs and limitations under which each work."

The Symposium was structured around seven general topics (the various sessions), seven invited speakers on these or more global issues, the Wayne Stinchcomb Memorial Award and Lecture, and a wrap-up panel discussion with the invited speakers. The following paragraphs provide brief overviews of all of the papers included in this STP. as well as comments on the panel discussion and additional oral presentations given during the Symposium.

Professor Paul Lagace opened the Symposium with an invited talk on "Technology Transition in the World of Composites--An Academic's Perspective." Professor Lagace provided the attendees with an insightful and entertaining overview of some of the more popular composite structures research topics over the years, and some of the resulting successes and/or barriers to practical use. No technical publication in this STP was warranted for Prof. Lagace's editorial subject.

Structural Damage Tolerance
Lincoln USAF/ASC, gave an invited talk and related paper that reviews the development of procedures used by the United States Air Force in the qualification of composite structures. He also reviews Navy programs, and the resulting Joint Service Specification Guide. The challenges in future certification initiatives, in particular, the need to reduce cost and address changes in manufacturing processes are discussed. He proposes a re-examination of the building-block process and a critical review of probabilistic methods.

Dr. [~qrl 3' Ilcewicz, FAA National Resource Specialist for Composites, gave an invited talk on his previously published "Perspectives on Large Flaw Behavior for Composite Aircraft Structure.'" This presentation gave an authoritative overview of low-velocity impact and discrete source damage threats, certification requirements, and structural response. No technical publication of this work was possible for this STP.

Olsson, Asp, Nilsson, and Sjogren review, in the main work performed at the Aeronautical Research Institute of Sweden (FFA), of studying the effects of impact upon composite structures. Both damage resistance and danrage tolerance are studied, along with an assessment of the effects of global buckling.

Anderson presented a practical approach to design-specific compression strength-after-impact certification. The application cited was that of a carbon/thermoplastic light helicopter tailboom.

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Functional Dyes Edited by Sung-Hoon Kim

Functional Dyes

Edited by Sung-Hoon Kim

Table of Contents

Recent Progress in Phthalocyanine Chemistry: Synthesis and Characterization (N.Kobayashi, T. Fukuda).
Cyanine Dyes for Solar Cells and Optical Data Storage (H. Tian, F. Meng).
Photochromic Naphthopyrans (J.D. Hepworth, B.M. Heron).
Cyanine Dyes as Fluorescent Non-covalent Labels for Nucleic Acid Research (T. Deligeorgiev, A. Vasilev).
Functional Dyes For Surface Plasmon Resonance-Based Sensing System (S.H. Kim, K. Koh).
Synthesis and Application of Squarylium Dyes (S. Yagi, H. Nakazumi).
Fluorine-containing Dyes (M. Matsui).

Preface
For a long time, organic dyes from our surroundings have been used to impart coloration effects to textiles and polymer substrates. These colored materials greatly influence our emotions and aesthetic satisfactions. Traditionally, organic dyes have been used for coloration, especially of textiles, by means of dyeing technology. However, nowadays, organic colorants have become increasingly important for high-technology applications in new fields such as electronic materials, devices, reprographics, and so on. These organic materials are called functional dyes.

There are a great number of books concerning dyes and pigments and they deal with a variety of subjects such as its synthesis, property, application, and analysis. However, few books have been written on functional dyes with respect to recent interesting research trends. For that reason, this book is considered to be necessary for the readers engaged in university, research institute, and industry so as to improve their fundamental knowledge and have wider appreciation for functional dyes. In addition, this book is to provide information on the latest developments and future directions in the functional dye chemistry. In general, dyes showing brilliant and beautiful colors with higher fastness properties are of great demand because of their suitability for various end-uses. Various numbers of chromophore have been investigated to achieve satisfactory characteristics in terms of functional applications and specialized uses. In this context, the special effects of organic colorants have been reevaluated and employed in the new areas of information-recording materials, information-display media, or optoelectronic devices. These dyes can also be applied to organic photoconductors, solar-energy utilizations, sensitizers, biomedical probe, photocatalysts, and so on. These new trends of dye chemistry have been recently developed and these classes of dyes are of significant importance in high-technology industries.

This book addresses various knowledge and information about functional dyes. It reviews recent advances on synthesis and characteristics of the functional dyes and their applications in high-technology uses. Furthermore, it provides a broad and interesting introduction to the science and technology of the applications of functional dyes. It will be a valuable information source for readers in that this book was peer-reviewed and written by special dye chemists around the world. The first chapter of the book deals with the recent progress in phthalocyanine chemistry. The second chapter covers the structure and properties of cyanine dyes for solar cells and optical data storage. The third chapter presents the synthesis and characterization of photochromic naphthopyrans, and Chapter 4 deals with the synthesis and appUcation of cyanine dyes as fluorescent non-covalent labels for nucleic acid research. Chapter 5 covers the surface plasmon resonance- based sensing system using functional dyes. In Chapter 6, the synthesis and application of squarylium dyes is described. The structures and physical properties of fluorine-containing dye are included in Chapter 7.

Thus, the main intention in preparing this book is to provide a fundamental understanding and an overview of the theories of dye chemistry for color chemists, organic chemists, and material scientists. It is hoped that it will also be useful for postgraduate students in chemistry and material science.

It is a pleasure to gratefully acknowledge the contributors of each chapter and their great enthusiasm in spite of their very busy schedules.

S.H. Kim

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

Handbook of Industrial Engineering Equations, Formulas, and Calculations

by Adedeji Badiru and 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
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

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