Residual Lifetime Prediction with Multistage Stochastic Degradation for Equipment

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Estimation value of posterior</td><td class="align_center" colspan="4"><i>t</i>/shots</td></tr><tr class="thead"><td class="align_center">1000</td><td class="align_center">2000</td><td class="align_center">3000</td><td class="align_center">4000</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"><svg height="11.6425pt" id="M131" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 16.7612 11.6425" width="16.7612pt" 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="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.58,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.376,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg> (10<sup>–5</sup>)</td><td class="align_center">1.7710</td><td class="align_center">2.2710</td><td class="align_center">2.7710</td><td class="align_center">0.9071</td></tr><tr><td class="align_left"><svg height="11.6425pt" id="M132" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 16.2784 11.6425" width="16.2784pt" 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="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.101,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.897,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg> (10<sup>–5</sup>)</td><td class="align_center">1.3020</td><td class="align_center">1.0007</td><td class="align_center">0.9785</td><td class="align_center">2.0572</td></tr><tr><td class="align_left"><svg height="11.6425pt" id="M133" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 15.4564 11.6425" width="15.4564pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.282,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.078,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg> (10<sup>–5</sup>)</td><td class="align_center">3.1618</td><td class="align_center">3.1128</td><td class="align_center">3.0862</td><td class="align_center">5.6825</td></tr><tr><td class="align_left"><svg height="11.6425pt" id="M134" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 17.4006 11.6425" width="17.4006pt" 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="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.215,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.011,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg> (10<sup>–4</sup>)</td><td class="align_center">0.7612</td><td class="align_center">0.7274</td><td class="align_center">0.6606</td><td class="align_center">1.6197</td></tr><tr><td class="align_left">RL (10<sup>4</sup>/shot)</td><td class="align_center">2.832</td><td class="align_center">2.724</td><td class="align_center">2.603</td><td class="align_center">2.470</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Updated hyperparameters based on the Bayesian method (1st stage).</div>

Complexity

tab3

Table 3

Table 3: Residual Lifetime Prediction with Multistage Stochastic Degradation for Equipment 