Novel Complexity Indicator of Manufacturing Process Chains and Its Relations to Indirect Complexity Indicators

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Complexity</td><td class="align_center">Metric by <br/>Frizelle</td><td class="align_center">Metric by <br/>Zhang</td><td class="align_center">Proposed metric</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><span style="width: 21.7719ptpx;"><svg height="12.9866pt" id="M73" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 21.7719 12.9866" width="21.7719pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z" id="g113-73"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="840" vert-adv-y="840" xpluscharwidth="10.92"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="14.50668539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.507,3.132)"><path d="M120 417C85 417 60 392 60 356S85 295 119 295S178 320 178 356S153 417 120 417ZM100 135C73 135 48 117 48 91C48 73 56 65 62 64C96 56 125 33 125 -4C125 -42 97 -68 46 -89L59 -124C123 -105 195 -59 195 22C195 94 137 135 100 135Z" id="g50-60"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="16.66369289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.663,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="21.094685390000002"></glyph.data></g></svg></span></td><td class="align_center">0 bits</td><td class="align_center">1 bit</td><td class="align_center">0 bits</td></tr><tr><td class="align_left"><span style="width: 21.7719ptpx;"><svg height="12.9866pt" id="M74" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 21.7719 12.9866" width="21.7719pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z" id="g113-73"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="840" vert-adv-y="840" xpluscharwidth="10.92"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="14.50668539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.507,3.132)"><path d="M120 417C85 417 60 392 60 356S85 295 119 295S178 320 178 356S153 417 120 417ZM100 135C73 135 48 117 48 91C48 73 56 65 62 64C96 56 125 33 125 -4C125 -42 97 -68 46 -89L59 -124C123 -105 195 -59 195 22C195 94 137 135 100 135Z" id="g50-60"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="16.66369289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.663,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="21.094685390000002"></glyph.data></g></svg></span></td><td class="align_center">1 bit</td><td class="align_center">2 bits</td><td class="align_center">1 bit</td></tr><tr><td class="align_left">Proof</td><td class="align_center"><span style="width: 58.3676ptpx;"><svg height="12.9866pt" id="M75" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 58.3676 12.9866" width="58.3676pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z" id="g113-73"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="840" vert-adv-y="840" xpluscharwidth="10.92"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="14.50668539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.507,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="16.66369289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.663,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="21.094685390000002"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.266,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="32.897"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,36.529,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z" id="g113-73"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="840" vert-adv-y="840" xpluscharwidth="47.449000000000005"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,46.604,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="51.03568539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,51.036,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" 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Static complexity values and their proof.

Complexity

tab2

Table 2

Table 2: Novel Complexity Indicator of Manufacturing Process Chains and Its Relations to Indirect Complexity Indicators 